Spherical functions on mixed symmetric spaces

Krötz, Bernhard; Neeb, Karl-Hermann; Ólafsson, Gestur

doi:10.1090/S1088-4165-01-00126-1

Spherical functions on mixed symmetric spaces
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by Bernhard Krötz, Karl-Hermann Neeb and Gestur Ólafsson

Represent. Theory 5 (2001), 43-92

DOI: https://doi.org/10.1090/S1088-4165-01-00126-1

Published electronically: April 23, 2001

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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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Abstract: