Spherical representations and mixed symmetric spaces

Krötz, Bernhard; Neeb, Karl-Hermann; Ólafsson, Gestur

doi:10.1090/S1088-4165-97-00035-6

Spherical representations and mixed symmetric spaces
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by Bernhard Krötz, Karl-Hermann Neeb and Gestur Ólafsson

Represent. Theory 1 (1997), 424-461

DOI: https://doi.org/10.1090/S1088-4165-97-00035-6

Published electronically: December 10, 1997

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Abstract:

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 $\Xi$ containing $G/H$ as a boundary component. The domain $\Xi$ is an orbit of an Ol’shanskii type semi group $\Gamma$. We describe the structure of the group $G$ and the domain $\Xi$. Furthermore we explore the correspondence between $\Gamma$-modules of holomorphic sections of line bundles over $\Xi$ and spherical highest weight modules.

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