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.
