Irreducible characters of and dimensions of spaces of fixed vectors

摘要

In this paper, we compute the conjugacy classes and the list of irreducible characters of , where is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of , where is a non-archimedean local field of characteristic zero with residue field of order .