Publications
Prof. Dr. Karl-Hermann Neeb
Publications
Articles in Journals
2024
Modular geodesics and wedge domains in non-compactly causal symmetric spaces
In: Annals of Global Analysis and Geometry 65 (2024), Article No.: 9
ISSN: 0232-704X
DOI: 10.1007/s10455-023-09937-6
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2023
From Euler Elements and 3-Gradings to Non-Compactly Causal Symmetric Spaces
In: Journal of Lie Theory 33 (2023), p. 377-432
ISSN: 0949-5932
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2022
Reflection positivity and Hankel operators— The multiplicity free case
In: Journal of Functional Analysis 283 (2022), Article No.: 109493
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2022.109493
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A family of non-modular covariant AQFTs
In: Analysis and Mathematical Physics 12 (2022), Article No.: 124
ISSN: 1664-2368
DOI: 10.1007/s13324-022-00727-0
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Semigroups in 3-graded Lie groups and endomorphisms of standard subspaces
In: Kyoto Journal of Mathematics 62 (2022), p. 577-613
ISSN: 2156-2261
DOI: 10.1215/21562261-2022-0017
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Wedge Domains in Compactly Causal Symmetric Spaces
In: International Mathematics Research Notices (2022)
ISSN: 1073-7928
DOI: 10.1093/imrn/rnac131
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Ground state representations of topological groups
In: Mathematische Annalen (2022)
ISSN: 0025-5831
DOI: 10.1007/s00208-022-02531-4
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2021
Central Extensions of Lie Groups Preserving a Differential Form
In: International Mathematics Research Notices 2021 (2021), p. 3794-3821
ISSN: 1073-7928
DOI: 10.1093/imrn/rnaa085
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Covariant Homogeneous Nets of Standard Subspaces
In: Communications in Mathematical Physics (2021)
ISSN: 1432-0916
DOI: 10.1007/s00220-021-04046-6
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FINITE DIMENSIONAL SEMIGROUPS OF UNITARY ENDOMORPHISMS OF STANDARD SUBSPACES
In: Representation Theory 25 (2021), p. 300-343
ISSN: 1088-4165
DOI: 10.1090/ert/566
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Elements in Pointed Invariant Cones in Lie Algebras and Corresponding Affine Pairs
In: Bulletin of the Iranian Mathematical Society (2021)
ISSN: 1735-8515
DOI: 10.1007/s41980-021-00671-y
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Nets of standard subspaces on Lie groups
In: Advances in Mathematics 384 (2021), Article No.: 107715
ISSN: 1090-2082
DOI: 10.1016/j.aim.2021.107715
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Standard Subspaces of Hilbert Spaces of Holomorphic Functions on Tube Domains
In: Communications in Mathematical Physics (2021)
ISSN: 0010-3616
DOI: 10.1007/s00220-021-04144-5
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2020
Covariant representations for possibly singular actions on C*-algebras
In: Dissertationes Mathematicae (2020), p. 1-94
ISSN: 0012-3862
DOI: 10.4064/dm793-6-2019
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CROSSED PRODUCTS OF C*-ALGEBRAS FOR SINGULAR ACTIONS WITH SPECTRUM CONDITIONS
In: Journal of Operator Theory 84 (2020), p. 369-451
ISSN: 0379-4024
DOI: 10.7900/jot.2019jun14.2265
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Multiplicity-freeness of Unitary Representations in Sections of Holomorphic Hilbert Bundles
In: International Mathematics Research Notices 2020 (2020), p. 4852-4889
ISSN: 1073-7928
DOI: 10.1093/imrn/rny160
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A survey on invariant cones in infinite dimensional lie algebras
In: Journal of Lie Theory 30 (2020), p. 513-564
ISSN: 0949-5932
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Universal central extensions of current Lie superalgebras
In: Journal of Pure and Applied Algebra 224 (2020)
DOI: 10.1016/j.jpaa.2019.106205
URL: https://arxiv.org/abs/1707.00282
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Reflection positivity on spheres
In: Analysis and Mathematical Physics 10 (2020), Article No.: 9
ISSN: 1664-2368
DOI: 10.1007/s13324-019-00353-3
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SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS
In: Transformation Groups (2020)
ISSN: 1083-4362
DOI: 10.1007/s00031-020-09595-z
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2019
Projective unitary representations of infinite-dimensional Lie groups
In: Kyoto Journal of Mathematics 59 (2019), p. 293-341
ISSN: 2156-2261
DOI: 10.1215/21562261-2018-0016
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KMS conditions, standard real subspaces and reflection positivity on the circle group
In: Pacific Journal of Mathematics 299 (2019), p. 117–169
ISSN: 0030-8730
DOI: 10.2140/pjm.2019.299.117
URL: https://arxiv.org/abs/1611.00080
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2018
Reflection positivity on real intervals
In: Semigroup Forum 96 (2018), p. 31-48
ISSN: 0037-1912
DOI: 10.1007/s00233-017-9847-8
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Erratum: Full regularity for a C-algebra of the canonical commutation relations
In: Reviews in Mathematical Physics 30 (2018)
ISSN: 0129-055X
DOI: 10.1142/S0129055X17920027
URL: https://arxiv.org/abs/math/0605413
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On the first order cohomology of infinite dimensional unitary groups
In: Annales de l'Institut Fourier 68 (2018), p. 2149-2176
ISSN: 0373-0956
DOI: 10.5802/aif.3205
URL: https://arxiv.org/abs/1607.00181
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Reflection negative kernels and fractional Brownian motion
In: Symmetry 10 (2018)
ISSN: 2073-8994
DOI: 10.3390/sym10060191
URL: https://arxiv.org/abs/1805.02593
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Half-Lie Groups
In: Transformation Groups 23 (2018), p. 801-840
ISSN: 1083-4362
DOI: 10.1007/s00031-018-9485-6
URL: https://arxiv.org/abs/1607.07728
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Reflection Positivity
In: Oberwolfach reports 14 (2018), p. 3263–3343
ISSN: 1660-8933
DOI: 10.4171/OWR/2017/55
URL: https://www.ems-ph.org/journals/show_abstract.php?issn=1660-8933&vol=14&iss=4&rank=10
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Current superalgebras and unitary representations
In: Journal of Pure and Applied Algebra 222 (2018), p. 3303-3333
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2017.12.009
URL: https://arxiv.org/abs/1707.00282
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2017
Isomorphisms of twisted Hilbert loop algebras
In: Canadian Journal of Mathematics-Journal Canadien De Mathematiques (2017)
ISSN: 0008-414X
DOI: 10.4153/CJM-2016-003-x
URL: https://arxiv.org/abs/1508.07938
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Diffeomorphism groups of compact convex sets
In: Indagationes Mathematicae 28 (2017), p. 760-783
ISSN: 0019-3577
DOI: 10.1016/j.indag.2017.04.004
URL: https://arxiv.org/abs/1603.05995
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Positive energy representations of double extensions of Hilbert loop algebras
In: Journal of the Mathematical Society of Japan 69 (2017), p. 1485-1518
ISSN: 0025-5645
DOI: 10.2969/jmsj/06941485
URL: https://arxiv.org/abs/1511.03980
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Smoothing operators and C*-algebras for infinite dimensional Lie groups
In: International Journal of Mathematics 28 (2017)
ISSN: 0129-167X
DOI: 10.1142/S0129167X17500422
URL: https://arxiv.org/abs/1505.02659
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2016
Polynomial representations of C*-algebras and their applications
In: Integral Equations and Operator Theory 86 (2016), p. 545-578
ISSN: 0378-620X
DOI: 10.1007/s00020-016-2335-9
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Reflection positive stochastic processes indexed by Lie groups
In: Symmetry Integrability and Geometry-Methods and Applications 12 (2016)
ISSN: 1815-0659
DOI: 10.3842/SIGMA.2016.058
URL: https://arxiv.org/abs/1510.07445
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Positive energy representations for locally finite split Lie algebras
In: International Mathematics Research Notices 21 (2016), p. 6689-6712
ISSN: 1073-7928
DOI: 10.1093/imrn/rnv367
URL: https://arxiv.org/abs/1507.06077
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Crossed product algebras and direct integral decomposition for Lie supergroups
In: Pacific Journal of Mathematics 282 (2016), p. 213-232
ISSN: 0030-8730
DOI: 10.2140/pjm.2016.282.213
URL: https://arxiv.org/abs/1506.01558
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On the characterization of trace class representations and Schwartz operators
In: Journal of Lie Theory 26 (2016), p. 787 - 805
ISSN: 0949-5932
URL: https://arxiv.org/abs/1512.02451
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2015
Finite dimensional compact and unitary Lie superalgebras
In: Journal of Pure and Applied Algebra 219 (2015), p. 4422 - 4440
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2015.02.024
URL: http://www.sciencedirect.com/science/article/pii/S0022404915000511
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Nonlinear completely positive maps and dilation theory for real involutive algebras
In: Integral Equations and Operator Theory 83 (2015), p. 517 - 562
ISSN: 0378-620X
DOI: 10.1007/s00020-015-2244-3
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Norm continuous unitary representations of Lie algebras of smooth sections
In: International Mathematics Research Notices (2015), p. 9081 - 9137
ISSN: 1073-7928
DOI: 10.1093/imrn/rnu231
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Integrability of unitary representations on reproducing kernel spaces
In: Representation Theory (2015), p. 24 - 55
ISSN: 1088-4165
DOI: 10.1090/S1088-4165-2015-00461-3
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Reflection positive one-parameter groups and dilations
In: Complex Analysis and Operator Theory 9 (2015), p. 653 - 721
ISSN: 1661-8254
DOI: 10.1007/s11785-014-0402-2
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Reflection positivity for the circle group
In: Journal of Physics : Conference Series 597 (2015), Article No.: 012004
ISSN: 1742-6588
DOI: 10.1088/1742-6596/597/1/012004
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C∗-algebras and direct integral decomposition for Lie supergroups
In: Pacific Journal of Mathematics 282 (2015), p. 213-232
ISSN: 0030-8730
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Classification of positive energy representations of the Virasoro group
In: International Mathematics Research Notices 18 (2015), p. 8620-8656
ISSN: 1073-7928
DOI: 10.1093/imrn/rnu197
URL: http://imrn.oxfordjournals.org/content/early/2014/11/08/imrn.rnu197
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On an invariance property of the space of smooth vectors
In: Kyoto Journal of Mathematics 55 (2015), p. 501 - 515
ISSN: 2156-2261
DOI: 10.1215/21562261-3089019
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2014
Crossed products of C*-algebras for singular actions
In: Journal of Functional Analysis 266 (2014), p. 5199 - 5269
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2014.01.022
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On convex hulls of orbits of Coxeter groups and Weyl groups
In: Münster Journal of Mathematics (2014), p. 463-487
ISSN: 1867-5778
DOI: 10.17879/58269762646
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Positive energy representations and continuity of projective representations for general topological groups
In: Glasgow Mathematical Journal 56 (2014), p. 295 - 316
ISSN: 0017-0895
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Semibounded unitary representations of double extensions of Hilbert-Loop groups
In: Annales de l'Institut Fourier 64 (2014), p. 1823 - 1892
ISSN: 0373-0956
URL: http://eudml.org/doc/275603
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Reflection positivity and conformal symmetry
In: Journal of Functional Analysis 206 (2014), p. 2174 - 2224
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2013.10.030
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2013
Infinite Tensor Products of C₀(R): Towards a Group Algebra for R∞
In: Journal of Operator Theory 70 (2013), p. 311 - 353
ISSN: 0379-4024
DOI: 10.7900/jot.2011aug22.1930
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Differentiable vectors and unitary representations of Fréchet-Lie supergroups
In: Mathematische Zeitschrift 275 (2013), p. 419-451
ISSN: 0025-5874
DOI: 10.1007/s00209-012-1142-5
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Positive definite superfunctions and unitary representations of Lie supergroups
In: Transformation Groups 18 (2013), p. 803-844
ISSN: 1083-4362
DOI: 10.1007/s00031-013-9228-7
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Making lifting obstructions explicit
In: Proceedings of the London Mathematical Society 106 (2013), p. 589 - 620
ISSN: 0024-6115
DOI: 10.1112/plms/pds047
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Oscillator algebras with semi-equicontinuous coadjoint orbits
In: Differential Geometry and its Applications 31 (2013), p. 268-283
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2012.10.010
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2012
Schur-Weyl Theory for C*-algebras
In: Mathematische Nachrichten 285 (2012), p. 1170 - 1198
ISSN: 0025-584X
DOI: 10.1002/mana.201100114
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When unit groups of continuous inverse algebras are regular Lie groups
In: Studia Mathematica 211 (2012), p. 95 - 109
ISSN: 0039-3223
URL: http://eudml.org/doc/285662
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Analytic extension techniques for unitary representations of Banach-Lie groups
In: International Mathematics Research Notices 18 (2012), p. 4260 - 4300
ISSN: 1073-7928
DOI: 10.1093/imrn/rnr174
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Categories of unitary representations of Banach-Lie supergroups and restriction functors
In: Pacific Journal of Mathematics 257 (2012), p. 431 - 469
ISSN: 0030-8730
DOI: 10.2140/pjm.2012.257.431
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Semibounded representations of Hermitian Lie groups
In: Travaux mathématiques 21 (2012), p. 29-109
ISSN: 1024-1833
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2011
On analytic vectors for unitary representations of infinite dimensional Lie groups
In: Annales de l'Institut Fourier 61 (2011), p. 1441 - 1476
ISSN: 0373-0956
URL: http://eudml.org/doc/219711
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Erratum: Cartan subalgebras of g∞
In: Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 54 (2011), p. 519
ISSN: 0008-4395
DOI: 10.4153/CMB-2011-018-2
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Borel-Weil Theory for Groups over Commutative Banach-Algebras
In: Journal für die reine und angewandte Mathematik 655 (2011), p. 165-187
ISSN: 0075-4102
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2010
Geometric characterization of hermitian algebras with continuous inversion
In: Bulletin of the Australian Mathematical Society 81 (2010), p. 96 - 113
ISSN: 0004-9727
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Localization via Automorphisms of the CARs: Local gauge invariance
In: Letters in Mathematical Physics 93 (2010), p. 169 - 185
ISSN: 0377-9017
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Borel-Weil theory for root graded Banach-Lie groups
In: International Mathematics Research Notices (2010), p. 783--823
ISSN: 1073-7928
DOI: 10.1093/imrn/rnp146
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On differentiable vectors for representations of infinite dimensional Lie groups
In: Journal of Functional Analysis 259 (2010), p. 2814 - 2855
ISSN: 0022-1236
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Semibounded representations and invariant cones in infinite dimensional Lie algebras
In: Confluentes Mathematici 2 (2010), p. 37--134
ISSN: 1793-7442
DOI: 10.1142/S1793744210000132
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An abstract settting for hamiltonian actions
In: Monatshefte für Mathematik 159 (2010), p. 261 - 288
ISSN: 0026-9255
DOI: 10.1007/s00605-009-0167-2
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2009
Full regularity for a C*-algebra of the canonical commutation relations
In: Reviews in Mathematical Physics 21 (2009), p. 587 - 613
ISSN: 0129-055X
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Pro-Lie groups which are infinite-dimensional Lie groups
In: Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), p. 351--378
ISSN: 0305-0041
DOI: 10.1017/S030500410800128X
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The compact generation of closed subgroups of locally compact groups
In: Journal of Group Theory 12 (2009), p. 555 - 559
ISSN: 1433-5883
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An implicit function theorem for Banach spaces and some applications
In: Mathematische Zeitschrift 262 (2009), p. 627 - 643
ISSN: 0025-5874
DOI: 10.1007/s00209-008-0394-6
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Central extensions of groups of sections
In: Annals of Global Analysis and Geometry 36 (2009), p. 381 - 418
ISSN: 0232-704X
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2008
Integration of locally exponential Lie algebras of vector fields
In: Annals of Global Analysis and Geometry 33 (2008), p. 89-100
ISSN: 0232-704X
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A nonsmooth continuous unitary representation of a Banach-Lie group
In: Journal of Lie Theory 18 (2008), p. 933--936
ISSN: 0949-5932
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Finite-dimensional Lie subalgebras of algebras with continuous inversion
In: Studia Mathematica 185 (2008), p. 249-262
ISSN: 0039-3223
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On the cohomology of vector fields on parallelizable manifolds
In: Annales de l'Institut Fourier 58 (2008), p. 1937--1982
ISSN: 0373-0956
URL: http://aif.cedram.org/item?id=AIF_2008__58_6_1937_0
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Closedness of the tangent spaces to the orbits of proper actions
In: Journal of Lie Theory 18 (2008), p. 517--521
ISSN: 0949-5932
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A complex semigroup approach to group algebras of infinite dimensional Lie groups
In: Semigroup Forum 77 (2008), p. 5-35
ISSN: 0037-1912
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Lie group extensions associated to projective modules of continuous inverse algebras
In: Archivum Mathematicum 44 (2008), p. 465--489
ISSN: 0044-8753
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On the classification of rational quantum tori and the structure of their automorphism groups
In: Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 51 (2008), p. 261 - 2812
ISSN: 0008-4395
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Lie Group structures on groups of smooth and holomorphic maps
In: Geometriae Dedicata 134 (2008), p. 17 - 60
ISSN: 0046-5755
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The second cohomology of current algebras of general Lie algebras
In: Canadian Journal of Mathematics-Journal Canadien De Mathematiques 60 (2008), p. 892--922
ISSN: 0008-414X
DOI: 10.4153/CJM-2008-038-6
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2007
Semi-edges, reflections and Coxeter groups
In: Transactions of the American Mathematical Society 359 (2007), p. 3647-3668
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-07-04040-8
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Non-abelian extensions of infinite-dimensional Lie groups
In: Annales de l'Institut Fourier 57 (2007), p. 209-271
ISSN: 0373-0956
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2006
Non-abelian extensions of topological Lie algebras
In: Communications in Algebra 34 (2006), p. 991-1041
ISSN: 0092-7872
DOI: 10.1080/00927870500441973
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On triples in the Shilov boundaries of bounded symmetric domains
In: Transformation Groups 11 (2006), p. 387-426
ISSN: 1083-4362
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A topological Maslov index for 3-graded Lie groups
In: Journal of Functional Analysis 233 (2006), p. 426-477
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2005.06.024
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2005
Projective Completions of Jordan Pairs, Part II: Manifold Structures and Symmetric Spaces
In: Geometriae Dedicata 112 (2005), p. 75-115
ISSN: 0046-5755
DOI: 10.1007/s10711-004-4197-6
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Addendum to "The universal central extension of the holomorphic current algebra"
In: Manuscripta Mathematica 116 (2005), p. 245-247
ISSN: 0025-2611
DOI: 10.1007/s00229-004-0510-9
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Derivations of locally simple Lie algebras
In: Journal of Lie Theory 15 (2005), p. 589-594
ISSN: 0949-5932
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2004
Projective completions of Jordan pairs. Part I: The generalized projective geometry of a Lie algebra
In: Journal of Algebra 277 (2004), p. 474-519
ISSN: 0021-8693
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Abelian extensions of infinite-dimensional Lie groups
In: Travaux mathématiques 15 (2004), p. 69-194
ISSN: 1024-1833
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2003
Banach-Lie quotients, enlargibility, and universal complexifications
In: Journal für die reine und angewandte Mathematik 560 (2003), p. 1-28
ISSN: 0075-4102
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Central extensions of current groups
In: Mathematische Annalen 326 (2003), p. 367-415
ISSN: 0025-5831
DOI: 10.1007/s00208-003-0425-x
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Locally convex root graded Lie algebras
In: Travaux mathématiques 14 (2003), p. 25-120
ISSN: 1024-1833
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On Cartan Subalgebras of gl∞
In: Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 46 (2003), p. 597-616
ISSN: 0008-4395
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Flux Homomorphisms and Principal Bundles over Infinite Dimensional Manifolds
In: Monatshefte für Mathematik 139 (2003), p. 309–333
ISSN: 0026-9255
DOI: 10.1007/s00605-002-0001-6
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The universal central extension of the holomorphic current algebra
In: Manuscripta Mathematica 112 (2003), p. 441-458
ISSN: 0025-2611
DOI: 10.1007/s00229-003-0409-x
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2002
Spherical Unitary Highest Weight Representations
In: Transactions of the American Mathematical Society 354 (2002), p. 1233-1264
ISSN: 0002-9947
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A Cartan–Hadamard Theorem for Banach–Finsler Manifolds
In: Geometriae Dedicata 95 (2002), p. 115-156
ISSN: 0046-5755
DOI: 10.1023/A:1021221029301
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Central extensions of infinite-dimensional Lie groups
In: Annales de l'Institut Fourier 52 (2002), p. 1365-1442
ISSN: 0373-0956
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Universal Central Extensions of Lie Groups
In: Acta Applicandae Mathematicae 73 (2002), p. 175-219
ISSN: 0167-8019
DOI: 10.1023/A:1019743224737
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Representations in L2-Spaces on Infinite-Dimensional Symmetric Cones
In: Journal of Functional Analysis 190 (2002), p. 133-178
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3884
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2001
Vector valued Riesz distributions on Euclidian Jordan algebras
In: Journal of Geometric Analysis 11 (2001), p. 43-75
ISSN: 1050-6926
DOI: 10.1007/BF02921953
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Spherical functions on mixed symmetric spaces
In: Representation Theory 5 (2001), p. 43-92
ISSN: 1088-4165
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Invariant symmetric bilinear forms for reflection groups
In: Journal of Geometry 71 (2001), p. 99-127
ISSN: 0047-2468
DOI: 10.1007/s00022-001-8556-2
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Compressions of infinite-dimensional bounded symmetric domains
In: Semigroup Forum 63 (2001), p. 71-105
ISSN: 0037-1912
DOI: 10.1007/s002330010037
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Locally finite Lie algebras with unitary highes weight representations
In: Manuscripta Mathematica 104 (2001), p. 343-358
ISSN: 0025-2611
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On the classification of locally finite split simple Lie algebras
In: Journal für die reine und angewandte Mathematik 533 (2001), p. 25-53
ISSN: 0075-4102
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2000
Positive definite spherical functions on Olshanski domains
In: Transactions of the American Mathematical Society 352 (2000), p. 1345--1380
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-99-02184-4
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Integrable roots in split graded Lie algebras
In: Journal of Algebra 225 (2000), p. 534--580
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8108
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Invariant orders on Lie groups and converings of ordered homogeneous spaces
In: Monatshefte für Mathematik 131 (2000), p. 123-153
ISSN: 0026-9255
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Representation theory and convexity
In: Transformation Groups 5 (2000), p. 325-350
ISSN: 1083-4362
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Smooth vectors for highest weight representations
In: Glasgow Mathematical Journal 42 (2000), p. 469-477
ISSN: 0017-0895
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Supplements to the papers entitled "On a Theorem of S. Banach" and "the separable representations of U(H)"
In: Journal of Lie Theory 10 (2000), p. 107-109
ISSN: 0949-5932
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1999
On the complex geometry of invariant domains in complexified symmetric spaces
In: Annales de l'Institut Fourier 49 (1999), p. 177--225
ISSN: 0373-0956
URL: http://www.numdam.org/item?id=AIF_1999__49_1_177_0
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1998
Holomorphic highest weight representations of infinite-dimensional complex classical groups
In: Journal für die reine und angewandte Mathematik 497 (1998), p. 171--222
ISSN: 0075-4102
DOI: 10.1515/crll.1998.038
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On the complex and convex geometry of Olshanski semigroups
In: Annales de l'Institut Fourier 48 (1998), p. 149--203
ISSN: 0373-0956
URL: http://www.numdam.org/item?id=AIF_1998__48_1_149_0
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On weighted Hardy spaces on complex semigroups
In: Semigroup Forum 56 (1998), p. 392--417
ISSN: 0037-1912
DOI: 10.1007/PL00005954
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Operator-valued positive definite kernels on tubes
In: Monatshefte für Mathematik 126 (1998), p. 125--160
ISSN: 0026-9255
DOI: 10.1007/BF01473583
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Unitary highest weight representations in Hilbert spaces of holomorphic functions on infinite-dimensional domains
In: Journal of Functional Analysis 156 (1998), p. 263--300
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3233
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1997
Spherical representations and mixed symmetric spaces
In: Representation Theory 1 (1997), p. 424--461 (electronic)
ISSN: 1088-4165
DOI: 10.1090/S1088-4165-97-00035-6
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A general non-linear convexity theorem
In: Forum Mathematicum 9 (1997), p. 613--640
ISSN: 0933-7741
DOI: 10.1515/form.1997.9.613
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Convexity properties of the coadjoint action of non-compact Lie groups
In: Mathematische Annalen 309 (1997), p. 625--661
ISSN: 0025-5831
DOI: 10.1007/s002080050131
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On a theorem of S. Banach
In: Journal of Lie Theory 7 (1997), p. 293--300
ISSN: 0949-5932
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On some classes of multiplicity free representations
In: Manuscripta Mathematica 92 (1997), p. 389--407
ISSN: 0025-2611
DOI: 10.1007/BF02678201
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On square integrable highest weight representations
In: Glasgow Mathematical Journal 39 (1997), p. 295--321
ISSN: 0017-0895
DOI: 10.1017/S0017089500032237
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1996
Orthogonal Lie algebras with cone potential
In: Communications in Algebra 24 (1996), p. 433--444
ISSN: 0092-7872
DOI: 10.1080/00927879608825579
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Spherical functions on Olshanski spaces
In: Journal of Functional Analysis 142 (1996), p. 446--493
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0156
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Conal Heisenberg algebras and associated Hilbert spaces
In: Journal für die reine und angewandte Mathematik 474 (1996), p. 67--112
ISSN: 1435-5345
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On hyperbolic cones and mixed symmetric spaces
In: Journal of Lie Theory 6 (1996), p. 69--146
ISSN: 0949-5932
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A note on central extensions of Lie groups
In: Journal of Lie Theory 6 (1996), p. 207--213
ISSN: 0949-5932
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Coherent states, holomorphic extensions, and highest weight representations
In: Pacific Journal of Mathematics 174 (1996), p. 497--542
ISSN: 0030-8730
URL: http://projecteuclid.org/euclid.pjm/1102365182
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Invariant convex sets and functions in Lie algebras
In: Semigroup Forum 53 (1996), p. 230--261
ISSN: 0037-1912
DOI: 10.1007/BF02574139
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Weakly exponential Lie groups
In: Journal of Algebra 179 (1996), p. 331--361
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0015
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Unitary highest weight representations via the orbit method I. The scalar case
In: Acta Applicandae Mathematicae 44 (1996), p. 151--184
ISSN: 0167-8019
DOI: 10.1007/BF00116520
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1995
Compression semigroups of open orbits in complex manifolds
In: Arkiv For Matematik 33 (1995), p. 293--322
ISSN: 0004-2080
DOI: 10.1007/BF02559711
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Compression semigroups of open orbits on real flag manifolds
In: Monatshefte für Mathematik 119 (1995), p. 187--214
ISSN: 0026-9255
DOI: 10.1007/BF01293670
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Groupoid C*-algebras of order compactified symmetric spaces
In: Japanese Journal of Mathematics 21 (1995), p. 117--188
ISSN: 0289-2316
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On the exponential function of an ordered manifold with affine connection
In: Mathematische Zeitschrift 218 (1995), p. 1--23
ISSN: 0025-5874
DOI: 10.1007/BF02571887
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Holomorphic Representation Theory I
In: Mathematische Annalen 301 (1995), p. 155-181
ISSN: 0025-5831
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Kähler structures and convexity properties of coadjoint orbits
In: Forum Mathematicum 7 (1995), p. 349-384
ISSN: 0933-7741
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On the convexity of the moment mapping for unitary highest weight representations
In: Journal of Functional Analysis 127 (1995), p. 301--325
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1014
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Maximality of compression semigroups
In: Semigroup Forum 50 (1995), p. 205--222
ISSN: 0037-1912
DOI: 10.1007/BF02573517
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Wiener-Hopf operators on ordered homogeneous spaces I
In: Journal of Functional Analysis 132 (1995), p. 86--118
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1101
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Epimorphisms of C*-algebras are surjective
In: Archiv der Mathematik 65 (1995), p. 134--137
ISSN: 0003-889X
DOI: 10.1007/BF01270691
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1994
Symplectic convexity theorems and coadjoint orbits
In: Compositio Mathematica 94 (1994), p. 129 - 180
ISSN: 0010-437X
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The geometry of nilpotent orbits of convex type in hermitian Lie algebras
In: Journal of Lie Theory 4 (1994), p. 185-235
ISSN: 0949-5932
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A convexity theorem for semisimple symmetric spaces
In: Pacific Journal of Mathematics 162 (1994), p. 305 - 349
ISSN: 0030-8730
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Contraction semigroups and representations
In: Forum Mathematicum 6 (1994), p. 233 - 270
ISSN: 0933-7741
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Correction to: ``A convexity theorem for semisimple symmetric spaces''
In: Pacific Journal of Mathematics 166 (1994), p. 401
ISSN: 0030-8730
URL: http://projecteuclid.org/euclid.pjm/1102621146
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Holomorphic Representation Theory II
In: Acta Mathematica 173 (1994), p. 103-133
ISSN: 0001-5962
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On closedness and simple connectedness of adjoint and coadjoint orbits
In: Manuscripta Mathematica 82 (1994), p. 51-65
ISSN: 0025-2611
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Representations of involutive semigroups
In: Semigroup Forum 48 (1994), p. 197 - 218
ISSN: 0037-1912
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The classification of Lie algebras with invariant cones
In: Journal of Lie Theory 4 (1994), p. 1-46
ISSN: 0949-5932
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1993
On wedges in Lie triple systems and ordered symmetric spaces
In: Geometriae Dedicata 46 (1993), p. 1 - 34
ISSN: 0046-5755
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1992
On the foundations of Lie semigroups
In: Journal für die reine und angewandte Mathematik (1992), p. 165 - 189
ISSN: 0075-4102
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On the fundamental group of a Lie semigroup
In: Glasgow Mathematical Journal (1992), p. 379 - 394
ISSN: 0017-0895
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The dualty between subsemigroups of Lie groups and monotone functions
In: Transactions of the American Mathematical Society 329 (1992), p. 653 - 677
ISSN: 0002-9947
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1991
Conal orders on homogeneous spaces
In: Inventiones Mathematicae 134 (1991), p. 467 - 496
ISSN: 0020-9910
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Monotone functions on symmetric spaces
In: Mathematische Annalen 291 (1991), p. 261 - 273
ISSN: 0025-5831
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Objects dual to subsemigroups of groups
In: Monatshefte für Mathematik 122 (1991), p. 303 - 321
ISSN: 0026-9255
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Semigroups in the universal covering group of SL (2)
In: Semigroup Forum 43 (1991), p. 33 - 43
ISSN: 0037-1912
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1990
Globality in semisimple Lie groups
In: Annales de l'Institut Fourier 40 (1990), p. 493-536
ISSN: 0373-0956
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Unpublished / Preprints
2024
Standard Subspaces in Quantum Field Theory and Representation Theory
2024
DOI: 10.14760/OWR-2023-50
URL: https://publications.mfo.de/handle/mfo/4092
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Contributions to Proceedings and Collections
2023
Algebraic Quantum Field Theory and Causal Symmetric Spaces
In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (ed.): Geometric Methods in Physics XXXIX. WGMP 2022, Springer Science and Business Media Deutschland GmbH, 2023, p. 207-231 (Trends in Mathematics, Vol.Part F1183)
DOI: 10.1007/978-3-031-30284-8_20
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2018
Kähler Geometry, Momentum Maps and Convex Sets
In: Yat-Sun Poon, Shing-Tung Yau, Lizhen Ji (ed.): Tsinghua Lectures in Mathematics, Boston: Higher Education Press in China International Press of Boston, 2018, p. 361-391 (Advanced Lectures in Mathematics ALM, Vol.45)
ISBN: 978-1571463722
URL: https://arxiv.org/abs/1510.03289
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On the geometry of standard subspaces
In: Jens Gerlach Christensen, Colgate University, Hamilton, NY, Susanna Dann, Vienna University of Technology, Wien, Austria and Matthew Dawson, CIMAT, Mérida, Mexico (ed.): Representation Theory, Symmetric Spaces, and Integral Geometry, 2018, p. 199-223 (Contemporary Mathematics, Vol.714)
ISBN: 978-1-4704-4070-1
DOI: 10.1090/conm/714
URL: https://arxiv.org/abs/1707.05506
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2017
50th Seminar Sophus Lie Seminar
In: K. Grabowska, J. Grabowski, A. Fialowski, K.-H. Neeb (ed.): Banach Center Publications, Polish Academy of Sciences, Warszawa, 2017
ISBN: 9788386806379
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Bounded and Semi-bounded Representations of Infinite Dimensional Lie Groups
In: Henning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb, Christoph Schweigert (ed.): Representation Theory - Current Trends and Perspectives, Zürich: European Mathematical Society EMS, 2017, p. 541-563 (EMS Congress Reports)
ISBN: 978-3-03719-171-2
DOI: 10.4171/171
URL: https://arxiv.org/abs/1510.08695
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Covariant central extensions of gauge Lie algebras
In: S. Albeverio, A. B. Cruzeiro, D. Holm (ed.): Stochastic Geometric Mechanics, Springer, 2017, p. 101-114 (Springer Proceedings in Mathematics & Statistics, Vol.202)
ISBN: 978-3-319-63452-4
URL: https://arxiv.org/abs/1510.07938
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Antiunitary representations and modular theory
In: 50th Seminar "Sophus Lie", 2017, p. 291-362 (Banach Center Publications, Vol.113)
DOI: 10.4064/bc113-0-16
URL: https://arxiv.org/abs/1704.01336
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2016
Momentum maps for smooth projective unitary representations
In: Kielanowski P., Bieliavsky P., Odesskii A., Odzijewicz A., Schlichenmaier M., Voronov T. (ed.): Geometric Methods in Physics. XXXIV Workshop 2015, Springer-Birkhäuser, 2016, p. 115-127 (Trends in Mathematics, Vol.II)
ISBN: 978-3-319-31755-7
DOI: 10.1007/978-3-319-31756-4_12
URL: https://arxiv.org/abs/1510.08257
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2015
Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions
In: V. Dobrev (ed.): Springer Proceedings in Mathematics & Statistics, Springer Japan, 2015, p. 105-136
ISBN: 978-4-431-55284-0
URL: https://arxiv.org/abs/1402.6818
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2014
Unitary representations of Unitary Groups
In: G. Mason, I. Penkov, J. Wolf (ed.): Lie theory workshops, Springer, 2014, p. 197 - 243 (Developmenst in Mathematics, Vol.37)
ISBN: 978-3-319-09933-0
DOI: 10.1007/978-3-319-09934-7_8
URL: https://arxiv.org/abs/1308.1500
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2013
Holomorphic Realization of Unitary Representations of Banach-Lie Groups
In: Huckleberry, A., Penkov, I., Zuckerman, G. (ed.): Lie Groups: Structure, Actions and Representations - In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday, New York: Springer, 2013, p. 185 - 223 (Progress in Mathematics, Vol.306)
ISBN: 978-1-4614-7192-9
DOI: 10.1007/978-1-4614-7193-6_10
URL: https://arxiv.org/abs/1011.1210
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2011
Lie groups of bundle automorphisms and their extensions
In: K.-H. Neeb; A. Pianzola (ed.): Developments and trends in infinite-dimensional Lie theory, Birkhäuser Boston, Inc., Boston, MA, 2011, p. 281--338 (Progr. Math., Vol.288)
DOI: 10.1007/978-0-8176-4741-4_9
URL: https://arxiv.org/abs/0709.1063
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Lie supergroups, unitary representations, and invariant cones
In: R. Fioresi, S. Ferrara, V.S. Varadarajan (ed.): Supersymmetry in mathematics and physics, Springer, Heidelberg, 2011, p. 195--239 (Lecture Notes in Math., Vol.2027)
DOI: 10.1007/978-3-642-21744-9_10
URL: https://arxiv.org/abs/1012.2809
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2010
Unitary highest weight modules of locally affine Lie algebras
In: Y. Gao et at (ed.): Quantum affine algebras, extended affine Lie algebras, and their applications, Amer. Math. Soc., Providence, RI, 2010, p. 227--262 (Contemp. Math., Vol.506)
DOI: 10.1090/conm/506/09943
URL: https://arxiv.org/abs/0904.0134
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2009
Semi-bounded unitary representations of infinite-dimensional Lie groups
In: J. Hilgert et al (ed.): Infinite dimensional harmonic analysis {IV}, World Sci. Publ., Hackensack, NJ, 2009, p. 209--222
DOI: 10.1142/9789812832825_0015
URL: https://arxiv.org/abs/0804.3484
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1998
Invariant cones in real representations
In: J. Hilgert et al. (ed.): Positivity in Lie theory: open problems, de Gruyter, Berlin, 1998, p. 99--119 (de Gruyter Expositions in Mathematics, Vol.26)
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Some open problems in representation theory related to complex geometry
In: Positivity in Lie theory: open problems, de Gruyter, Berlin, 1998, p. 195--220 (de Gruyter Exp. Math., Vol.26)
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1996
A Duistermaat-Heckman formula for admissible coadjoint orbits
In: H.-D. Doebner et al. (ed.): Lie theory and its applications in physics (Clausthal, 1995), World Sci. Publ., River Edge, NJ, 1996, p. 15--35
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1995
Symplectic convexity theorems, Lie semigroups, and unitary representations
In: K. H. Hofmann et al. (ed.): Semigroups in algebra, geometry and analysis (Oberwolfach, 1993), de Gruyter, Berlin, 1995, p. 201--240 (de Gruyter Expositions in Mathematics, Vol.20)
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Holomorphic representations of Olshanski semigroups
In: K.H. Hofmann et al. (ed.): Semigroups in algebra, geometry and analysis (Oberwolfach, 1993), de Gruyter, Berlin, 1995, p. 241--271 (de Gruyter Exp. Math., Vol.20)
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1994
Poisson Lie groups and non-linear convexity theorems
In: H.-D. Doebner et al. (ed.): Generalized symmetries in physics (Clausthal, 1993), World Sci. Publ., River Edge, NJ, 1994, p. 395--410
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Holomorphic representations and coherent states
In: J.-P. Antoine et al. (ed.): Quantization and infinite-dimensional systems (Bialowieza, 1993), Plenum, New York, 1994, p. 79--86
DOI: 10.1007/978-1-4615-2564-6_9
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A general setting for Wiener-Hopf operators
In: 75 years of Radon transform (Vienna, 1992), Int. Press, Cambridge, MA, 1994, p. 189--208 (Conf. Proc. Lecture Notes Math. Phys., IV)
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Books
2018
Reflection Positivity - A Representation Theoretic Perspective
Springer International Publishing, 2018
(Springer Briefs in Mathematical Physcis, Vol.32)
ISBN: 978-3-319-94754-9
DOI: 10.1007/978-3-319-94755-6
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2012
Structure and geometry of Lie groups
Springer, New York, 2012
(Springer Monographs in Mathematics)
ISBN: 978-0-387-84793-1
DOI: 10.1007/978-0-387-84794-8
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2000
Holomorphy and convexity in Lie theory
Walter de Gruyter & Co., Berlin, 2000
(Expositions in Mathematics, Vol.28)
ISBN: 3-11-015669-5
DOI: 10.1515/9783110808148
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1993
Lie Semigroups and their Applications
Springer-Verlag, 1993
(Lecture Notes in Math., Vol.1552)
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Invariant Subsemigroups of Lie Groups
1993
(Memoirs of the Amer. Math. Soc., Vol.499)
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1991
Lie-Gruppen und Lie-Algebren
Vieweg Verlag, 1991
(Memoirs of the American Mathematical Society)
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Edited Volumes
2017
Representation Theory - Current Trends and Perspectives
Zürich: 2017
(EMS Congress Reports)
ISBN: 978-3-03719-171-2
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, , , , (ed.):
50th Seminar "Sophus Lie" dedicated to Professor Karl Heinrich Hofmann on the occasion of his 85th birthday
2017
(Banach Center Publications, Vol. 113)
ISBN: 978-83-86806-37-9
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Thesis
1993
Holomorphic Representation Theory and Coadjoint Orbits of Convexity Type (Habilitation, 1993)
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1989
Globality of Lie Wedges (Dissertation, 1989)
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