Tamely ramified supercuspidal representations of GIn

Abstract

Let F be a non-Archimedean local field of residual characteristic p; then conjecturally the supercuspidal representations of Gln(F) are parameterized by admissible characters of extensions of F of degree n provided that n is prime to p. In this paper we establish the existence of the necessary representations if the conjecture is to be true. They will be realized as induced representations from certain subgroups, compact modulo the center. The more difficult question of whether all supercuspidal representations arise by this construction will not be treated. We will also leave aside the problem of computing the characters of these representations. © 1977, University of California, Berkeley. All Rights Reserved.