Irreducible non-cuspidal characters of GSp(4,Fq)

Abstract

Admissible non--supercuspidal representations of GSp(4,F), where F is a local field of characteristic zero with an odd-ordered residue field Fq, have finite dimensional spaces of fixed vectors under the action of principal congruence subgroups. We can say precisely what these dimensions are for nearly all local fields and principal congruence subgroups of level p by understanding the non-cuspidal representation theory of the finite group GSp(4,Fq). The conjugacy classes and the list of irreducible characters of this group are given. Genericity and cuspidality of the irreducible characters are also determined.