Intertwining and Supercuspidal Types for <i>p</i>-Adic Classical Groups

Abstract

Let F be a non-archimedean local field of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group, considered as the fixed point subgroup in G ~ = G L ( N , F ) of an involution σ. We generalize the notion of a simple character for G ~ , which was introduced by Bushnell and Kutzko [Annals of Mathematics Studies 129 (Princeton University Press, 1993)], to define semisimple characters. Given a semisimple character θ for G ~ fixed by σ, we transfer it to a character θ− for G and calculate its intertwining. If the torus associated to θ− is maximal compact, we obtain supercuspidal representations of G, which are new if the torus is split only over a wildly ramified extension. 2000 Mathematics Subject Classification: 22E50.