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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Spherical representations and mixed symmetric spaces
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by Bernhard Krötz, Karl-Hermann Neeb and Gestur Ólafsson PDF
Represent. Theory 1 (1997), 424-461 Request permission


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 $1 {\frac {1}{2}}$, 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