Supercuspidal Representations of GLn: Explicit Whittaker Functions
نویسندگان
چکیده
منابع مشابه
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...
متن کاملConstruction 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...
متن کاملSupercuspidal 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...
متن کاملWHITTAKER MODELS AND THE INTEGRAL BERNSTEIN CENTER FOR GLn
We establish integral analogues of results of Bushnell and Henniart [BH] for spaces of Whittaker functions arising from the groups GLn(F ) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the conjectural “local Langlands correspondence in families” of [EH], and reduce the question of the existence of such representations to a natural conjectur...
متن کاملTypes for supercuspidal representations of GL(N)
We recall here the basic definitions needed to construct simple types, with no proofs given of the many claims that we make. For a much more detailed account, see [1] and the many other sources cited therein. Note that most of the statements made here could be proven without much difficulty for the reader who has the time and inclination. Any statements requiring a much more elaborate proof are...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7542