For a p-adic field F of characteristic zero, the embeddings of a tame supercuspidal representation π of G = GLn(F ) in the space of smooth functions on the set of symmetric matrices in G are determined. It is shown that the space of such embeddings is nonzero precisely when −1 is in the kernel of π and, in this case, this space has dimension four. In addition, the space of H-invariant linear fo...

We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, any irreducible admissible representation of the symplectic similitude group GSp(V ) decomposes with multiplicity one when restricted to the symplectic group Sp(V ). We prove the analogous result for GO(V ) and O(V ), where V is an orthogonal space over k. Wh...

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 G̃ of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G̃ and for G. In particular, following the formalism of [4], we show that these semisimple characters h...

Abstract Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations Levi subgroups $\textrm {M}^{\prime}$ {SL}_n(F)$ is unique up to {M}^{\prime}$-conjugation, where $F$ either finite or non-Archimedean locally compact residual $p$.