  Let $G$ be a reductive $p$-adic group. We prove that all supercuspidal
representations of $G$ arise through Yu's construction subject to certain
hypotheses on $k$ (depending on $G$). 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.

Representation Theory