Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors

摘要

In this paper, we compute the conjugacy classes and the list of irreduciblecharacters of GSp(4,q), where q is odd. We also determine precisely whichirreducible characters are non-cuspidal and which are generic. These charactersare then used to compute dimensions of certain subspaces of fixed vectors ofsmooth admissible non-supercuspidal representations of GSp(4,F), where F is anon-archimedean local field of characteristic zero with residue field of orderq.