Spherical representations of the jacobi group

Abstract

LetG j be the Jacobi group over ap-adic field. By explicit calculations in certain models, spherical vectors for admissible Gj-representations are determined. This leads to a complete classification of spherical representations ofG j in the “almost good” case, and to a description of how these representations correspond to the characters of the Hecke algebra. This result is used to “explain” the local factors attached to a classical Jacobi eigenform of square free index by J. DULINSKI in [51].