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

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. 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, $\Bbb R$).