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Journal of the London Mathematical Society 2002 65(3):524-546; doi:10.1112/S0024610701002927
© 2002 by London Mathematical Society
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© The London Mathematical Society

Fourier–Jacobi Type Spherical Functions for PJ-Principal Series Representations of Sp(2, R)

Miki Hirano

Department of Mathematical Sciences, Faculty of Science, Ehime University Ehime 790-8577, Japan, hirano{at}math.sci.ehime-u.ac.jp

Received 1 March 2001. Revision received 16 July 2001.

The paper studies a generalized spherical function, or a generalized Whittaker model for generalized principal series representations of G=Sp(2, R) induced from the Jacobi maximal parabolic subgroup PJ, 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.


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