Supercuspidal representations: An exhaustion theorem

Abstract

Let G G be a reductive p p -adic group. We prove that all supercuspidal representations of G G arise through Yu’s construction subject to certain hypotheses on k k (depending on G G ). As a corollary, under the same hypotheses, we see that any supercuspidal representation is compactly induced from a representation of an open subgroup which is compact modulo the center.