This article is cited in 4 papers

Olshanski spherical pairs related to the Heisenberg group

Jacques Faraut

Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 place Jussieu, case 247, 75 252 Paris cedex 05, France

Abstract: 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.

Key words and phrases: Heisenberg group, spherical function, Jack polynomial, Laguerre polynomial.

MSC: 43A90, 22E27, 33C50

Received: July 6, 2010; in revised form June 20, 2013

Language: English

DOI: 10.17323/1609-4514-2014-14-1-63-81

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