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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 functions on mixed symmetric spaces
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by Bernhard Krötz, Karl-Hermann Neeb and Gestur Ólafsson PDF
Represent. Theory 5 (2001), 43-92 Request permission


In this article we compute the spherical functions which are associated to hyperbolically ordered symmetric spaces $H\backslash G$. These spaces are usually not semisimple; one prominent example is given by $H\backslash G= ({\mathbb R}^n\rtimes {\mathrm {Gl}}(n,{\mathbb R}))\backslash (H_n\rtimes {\mathrm {Sp}} (n,{\mathbb R}))$ with $H_n$ the $(2n+1)$-dimensional Heisenberg group.
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Additional Information
  • Bernhard Krötz
  • Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210–1174
  • Email:
  • Karl-Hermann Neeb
  • Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany
  • MR Author ID: 288679
  • Email:
  • Gestur Ólafsson
  • Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisianna 70803
  • MR Author ID: 133515
  • Email:
  • Received by editor(s): March 29, 2000
  • Received by editor(s) in revised form: September 26, 2000, and March 20, 2001
  • Published electronically: April 23, 2001
  • Additional Notes: The first author was supported by the DFG-project HI 412/5-2 and LSU
    The second author was supported by NSF grant DMS-9626541, DMS 0070607, INT 972277, and LEQSF grant (1996-99)-RD-A-12
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 43-92
  • MSC (2000): Primary 22E30, 22E45, 43A85
  • DOI:
  • MathSciNet review: 1826428