AG Lie-Gruppen: T. Simon, FAU: Asymptotic behavior of holomorphic extensions of orbit maps of K-finite vectors in principal series representations

Asymptotic behavior of holomorphic extensions of orbit maps of K-finite
vectors in principal series representations – Vortragender: Tobias Simon, FAU
Erlangen – Einladender: Karl-Hermann Neeb

Abstract: For semisimple Lie groups G and their associated Riemannian
symmetric space G/K, there is a domain called the complex crown domain closely
tied to the unitary representation theory of G. In this talk, we discuss the
Krotz-Stanton theorem which states that one can extend orbit maps of K-finite
vectors for irreducible unitary representations of G to a particular
holomorphic vector bundle over the crown. Motivated by realizations of
representations on bundle-valued distributions, we present asymptotic norm
estimates we obtained for the holomorphic extensions of orbit maps associated
to K-finite vectors in principal series representations. These norm estimates
are crucial in proving the existence of the limits of the extended orbit maps
in the space of distribution vectors as one approaches the boundary of the
crown.