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Matrix coefficients of the large discrete series representations of Sp(2; R) as hypergeometric series of two variables

Published online by Cambridge University Press:  11 January 2016

Takayuki Oda
Takayuki Oda*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro-Ku, Tokyo 153-8914Japan, takayuki@ms.u-tokyo.ac.jp
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Abstract

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We investigate the radial part of the matrix coefficients with minimal K-types of the large discrete series representations of Sp(2; R). They satisfy certain difference-differential equations derived from Schmid operators. This system is reduced to a holonomic system of rank 4, which is finally found to be equivalent to higher-order hypergeometric series in the sense of Appell and Kampé de Fériet.

Keywords

22E3022E4543A9033C65
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 208: Memorial Volume for Professor Hiroshi Saito , December 2012 , pp. 201 - 263
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

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