Spherical representations and mixed symmetric spaces
Let G/H be a symmetric space admitting a G-invariant hyperbolic cone field. For each such cone field we construct a local tube domain Ξ containing G/H as a boundary component. The domain Ξ is an orbit of an Ol’shanskii type semi group Γ. We describe the structure of the group G and the domain Ξ. Furthermore we explore the correspondence between Γ-modules of holomorphic sections of line bundles over Ξ and spherical highest weight modules. © 1997 American Mathematical Society.
Publication Source (Journal or Book title)
Krötz, B., Neeb, K., & Ólafsson, G. (1997). Spherical representations and mixed symmetric spaces. Representation Theory, 1 (15), 424-461. https://doi.org/10.1090/S1088-4165-97-00035-6