WHITTAKER MODELS AND THE INTEGRAL BERNSTEIN CENTER FOR GLn
نویسنده
چکیده
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 conjecture relating the integral Bernstein center of GLn(F ) to the deformation theory of Galois representations.
منابع مشابه
Generalized and Degenerate Whittaker Models
We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model corresponding to a nilpotent orbit to any degenerate Whittaker model corresponding to the same orbit, and to certain degenerate Whittaker models corresponding ...
متن کاملGauss Sum Combinatorics and Metaplectic Eisenstein Series
1.1. Steve Gelbart, Whittaker models and the metaplectic group. The metaplectic double cover of Sp(2r) and the Weil representation were introduced by Weil [37] in order to formulate results of Siegel on theta functions in the adelic setting. This was followed by two initially independent developments. First, Shimura [32], [33] gave two extremely important constructions involving modular forms o...
متن کاملM ay 2 00 5 Whittaker and Bessel functors for G S p 4
The theory of Whittaker functors for GLn is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([5]). We define Whittaker functors for GSp 4 and study their properties. These functors correspond to the maximal parabolic subgroup of GSp 4 , whose unipotent radical is not commutative. We also study similar functors cor...
متن کاملAn Integral Representation of Standard Automorphic L Functions for Unitary Groups
Let F be a number field, G the general linear group of degree n defined over F. Let π be an irreducible cuspidal automorphic representation of G(A). In [1–3], a Rankin-Selbergtype integral is constructed to represent the L function of π. That the integrals of Jacquet, Piatetski-Shapiro, and Shalika are Eulerian follows from the uniqueness of Whittaker models and the fact that cuspidal represent...
متن کامل0 A ug 2 00 4 Whittaker and Bessel functors for G S p 4
1.1 Whittaker and Bessel models are of importance in the theory of automorphic representations of GSp4. This paper is the first in a series of two, where we study some phenomena corresponding to these models in the geometric Langlands program. The theory of Whittaker functors for GLn is an essential technical tool in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langl...
متن کامل