Moscow Mathematical Journal

Volume 14, Issue 1, January–March 2014 pp. 63–81.

Olshanski Spherical Pairs Related to the Heisenberg Group

Authors: Jacques Faraut
Author institution: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 place Jussieu, case 247, 75 252 Paris cedex 05, France
Summary:

An Olshanski spherical pair (G, K) is the inductive limit of a sequence of Gelfand pairs (G(n), K(n)). A natural question arises: how a spherical function for (G, K) can be obtained as limit of spherical functions for (G(n), K(n)). In this paper we consider a sequence of Gelfand pairs (G(n), K(n)) related to the Heisenberg group.

2010 Mathematics Subject Classification. 43A90, 22E27, 33C50.

Keywords: Heisenberg group, spherical function, Jack polynomial, Laguerre polynomial.

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