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FOURIER–JACOBI TYPE SPHERICAL FUNCTIONS FOR $P_J$-PRINCIPAL SERIES REPRESENTATIONS OF ${\rm Sp}(2, {\bf R})$

Published online by Cambridge University Press:  24 March 2003

MIKI HIRANO
MIKI HIRANO
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ehime University, Ehime 790-8577, Japanhirano@math.sci.ehime-u.ac.jp
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Abstract

The paper studies a generalized spherical function, or a generalized Whittaker model for generalized principal series representations of $G={\rm Sp}(2,{\bf R})$ induced from the Jacobi maximal parabolic subgroup $P_{\rm J}$ , which is called the Fourier–Jacobi type. In particular, a multiplicity theorem and an explicit formula via the Meijer $G$ -functions for this function are given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 524 - 546
Copyright
The London Mathematical Society, 2002

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