On the construction of tame supercuspidal representations

Abstract

Let $F$ be a non-archimedean local field of residual characteristic $p \neq 2$ . Let $G$ be a (connected) reductive group over $F$ that splits over a tamely ramified field extension of $F$ . We revisit Yu's construction of smooth complex representations of $G(F)$ from a slightly different perspective and provide a proof that the resulting representations are supercuspidal. We also provide a counterexample to Proposition 14.1 and Theorem 14.2 in Yu [ Construction of tame supercuspidal representations , J. Amer. Math. Soc. 14 (2001), 579–622], whose proofs relied on a typo in a reference.