Intertwining and Supercuspidal Types for p ‐Adic Classical Groups

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 inG ~ = G L ( N , F ) of an involution σ. We generalize the notion of a simple character forG ~ , 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 forG ~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.