## 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.## References

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## Bibliographic Information

**Bernhard Krötz**- Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse $1 {\frac {1}{2}}$, D-91054 Erlangen, Germany
**Karl-Hermann Neeb**- Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse $1 {\frac {1}{2}}$, D-91054 Erlangen, Germany
- MR Author ID: 288679
**Gestur Ólafsson**- Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse $1 {\frac {1}{2}}$, D-91054 Erlangen, Germany; Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- MR Author ID: 133515
- Received by editor(s): June 24, 1997
- Received by editor(s) in revised form: September 25, 1997
- Published electronically: December 10, 1997
- © Copyright 1997 American Mathematical Society
- Journal: Represent. Theory
**1**(1997), 424-461 - MSC (1991): Primary 22E47, 22E15, 53C35, 54H15
- DOI: https://doi.org/10.1090/S1088-4165-97-00035-6
- MathSciNet review: 1483015