1 Se p 20 07 Distinguished Tame Supercuspidal Representations Jeffrey

TAME SUPERCUSPIDAL REPRESENTATIONS OF GLn DISTINGUISHED BY ORTHOGONAL INVOLUTIONS

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...

Murnaghan-kirillov Theory for Supercuspidal Representations of Tame General Linear Groups

Spherical characters: the supercuspidal case

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation π of a connected reductive p-adic group, subject to the assumption that π is obtained via induction from a representation of an open compact mod centre subgroup. We derive an integral formula for each spherical character belonging to the the basis. This formula involves integration of a part...

Construction of Tame Supercuspidal Representations

The notion of depth is defined by Moy-Prasad [MP2]. The notion of a generic character will be defined in §9. When G = GLn or G is the multiplicative group of a central division algebra of dimension n with (n, p) = 1, our generic characters are just the generic characters in [My] (where the definition is due to Kutzko). Moreover, in these cases, our construction literally specializes to Howe’s c...

Supercuspidal Representations: an Exhaustion Theorem

Let k be a p-adic field of characteristic zero and residue characteristic p. Let G be the group of k-points of a connected reductive group G defined over k. In [38], Yu gives a fairly general construction of supercuspidal representations of G in a certain tame situation. In this paper, subject to some hypotheses on G and k, we prove that all supercuspidal representations arise through his const...