Supercuspidal support of irreducible modulo l-representations of SL_n(F)

Abstract

Let k be an algebraically closed field with characteristic l different from p. We show that the supercuspidal support of irreducible smooth k-representations of Levi subgroups M' of SL_n(F) is unique up to M'-conjugation, where F is either a finite field of characteristic p or a non-archimedean locally compact field of residual characteristic p.