Generalized and degenerate Whittaker models

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 ...

Degenerate Whittaker Functionals for Real Reductive Groups

In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups, thereby generalizing results of Kostant, Matumoto and others.

The Whittaker Models of Induced Representations

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.

Twisted Whittaker models for metaplectic groups

ON p-ADIC GENERALIZED WHITTAKER FUNCTIONS ON GSp(4)

Let G be a connected reductive algebraic group defined over a non-Archimedean local field F . The study of Whittaker functions on G has a long history. For example, if G = GL(2), an explicit formula for the Whittaker function is well-known (See [5]). Shintani proved an explicit formula for the case G = GL(n) and expressed it by Schur polynomials in [16]. Casselman and Shalika generalized Shinta...