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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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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
Published electronically: December 10, 1997


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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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:
  • MathSciNet review: 1483015