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Spherical representations and mixed symmetric spaces

Author(s): Bernhard Krötz; Karl-Hermann Neeb; Gestur Ólafsson
Journal: Represent. Theory 1 (1997), 424-461.
MSC (1991): Primary 22E47, 22E15, 53C35, 54H15
Posted: 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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Additional Information:

Bernhard Krötz
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany

Karl-Hermann Neeb
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany

Gestur Ólafsson
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany - Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803

DOI: 10.1090/S1088-4165-97-00035-6
PII: S 1088-4165(97)00035-6
Received by editor(s): June 24, 1997
Received by editor(s) in revised form: September 25, 1997
Posted: December 10, 1997
Copyright of article: Copyright 1997, American Mathematical Society

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