Semisimple characters for p-adic classical groups

Abstract

Let G be a unitary, symplectic, or orthogonal group over a non-Archimedean local field of residual characteristic different from 2, considered as the fixed-point subgroup in a general linear group $\widetilde{G}$ of an involution. Following [8] and [12], we generalize the notion of a semisimple character for $\widetilde{G}$ and for G. In particular, following the formalism of [4], we show that these semisimple characters have certain functorial properties. Finally, we show that any positive level supercuspidal representation of G contains a semisimple character.