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Fourier–Jacobi Type Spherical Functions for Discrete Series Representations of Sp(2, $\Bbb R$)

Published online by Cambridge University Press:  04 December 2007

Miki Hirano
Miki Hirano
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ehime University, Ehime, 790-8577, Japan. E-mail: hirano@math.sci.ehime-u.ac.jp
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Abstract

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In this paper we define a kind of generalized spherical functions on Sp(2, $\Bbb R$). We call it ‘Fourier–Jacobi type’, since it can be considered as a generalized Whittaker model associated with the Jacobi maximal parabolic subgroup. Also we give the multiplicity theorem and an explicit formula of these functions for discrete series representations of Sp(2, $\Bbb R$).

Keywords

Fourier–Jacobi expansionJacobi groupMeijer's G-functiongeneralized Whittaker modeldiscrete series representation
Type
Research Article
Information
Compositio Mathematica , Volume 128 , Issue 2 , September 2001 , pp. 177 - 216
Copyright
© 2001 Kluwer Academic Publishers