AG Mathematische Physik, Ian Koot: Relative positions of Half-sided Modular Inclusions

Ian Koot

Relative positions of Half-sided Modular Inclusions

Abstract:
Half-sided Modular Inclusions are inclusions of standard subspaces
where the modular groups of the two standard subspaces satisfy some
‘nice’ relations. Recently we proved that inclusions of two standard
subspaces that lie as Half-sided Modular Inclusions in a larger standard
subspace can be fully characterized by inclusions of associated complex
subspaces. We use these results, together with the representation
theory of the Canonical Commutation Relations and the theory of Hardy
spaces, to clarify how two half-sided modular inclusions in the same
standard subspace can relate to each other.