AG Lie-Gruppen: T. Simon, FAU: Constructing Nets of Standard Subspaces on Non-Compactly Causal Symmetric Spaces from K-Finite Vectors in Unitary Representations

Constructing Nets of Standard
Subspaces on Non-Compactly Causal Symmetric Spaces from K-Finite Vectors in Unitary
Representations – Vortragender: Tobias Simon, FAU Erlangen-Nürnberg – Einladender: K.-H. Neeb

Abstract: In this talk, we discuss the construction from Frahm,
Neeb, and Olafsson of nets of standard subspaces on a non-compactly causal
symmetric space G/H associated to unitary representations of G, which satisfy
Isotony, Covariance, Reeh-Schlieder and the Bisognano-Wichmann property. Here,
one of the main difficulties is to guarantee the existence of cyclic
H-invariant finite-dimensional subspaces of distribution vectors. This is
achieved by proving distributional boundary values for the holomorphic
extension of orbit maps of K-finite vectors. These subspaces of distribution
vectors can be used to realize the representation in a space of distributional
sections and construct the net geometrically.