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Spherical functions on mixed symmetric spaces


Authors: Bernhard Krötz, Karl-Hermann Neeb and Gestur Ólafsson
Journal: Represent. Theory 5 (2001), 43-92
MSC (2000): Primary 22E30, 22E45, 43A85
DOI: https://doi.org/10.1090/S1088-4165-01-00126-1
Published electronically: April 23, 2001
MathSciNet review: 1826428
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Abstract:

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: kroetz@math.ohio-state.edu

Karl-Hermann Neeb
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany
Email: neeb@mathematik.tu-darmstadt.de

Gestur Ólafsson
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisianna 70803
Email: olafsson@math.lsu.edu

DOI: https://doi.org/10.1090/S1088-4165-01-00126-1
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
Article copyright: © Copyright 2001 American Mathematical Society

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