The Whittaker Models of Induced Representations
نویسنده
چکیده
If F is a local non-Archimedean field, then every irreducible admissible representation π of GL(r, F) is a quotient of a representation ξ induced by tempered ones. We show that £ has a Whittaker model, even though it may fail to be irreducible.
منابع مشابه
Generalized Whittaker functions on GSp(2,R) associated with indefinite quadratic forms
We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth propert...
متن کاملRepresentations of GL(2) and SL(2) over finite fields
Irreducible complex representations of GL(2) and SL(2) over a finite field can be classified by methods useful for p-adic reductive groups and real Lie groups. (See Piatetski-Shapiro’s inspiring A.M.S. Memoir on this subject.) That is, we first see that most principal series representations are irreducible. We determine the irreducible constituents of the irregular principal series. We prove th...
متن کاملGeneralized 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 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 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 کامل