Tame Cuspidal Representations in Non-Defining Characteristics

Abstract

Let F be a nonarchimedean local field of residual characteristic $\mathit{p}\ne 2$. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu’s construction of complex supercuspidal representations yields smooth, irreducible, cuspidal representations over an arbitrary algebraically closed field R of characteristic different from p. Moreover, we prove that this construction provides all smooth, irreducible, cuspidal R-representations if p does not divide the order of the Weyl group of G.