Whittaker models for real reductive groups

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.

Whittaker Supports for Representations of Reductive Groups

Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...

Twisted Whittaker models for metaplectic groups

Kazhdan’s Orthogonality Conjecture for Real Reductive Groups

We prove a generalization of Harish-Chandra’s character orthogonality relations for discrete series to arbitrary Harish-Chandra modules for real reductive Lie groups. This result is an analogue of a conjecture by Kazhdan for p-adic reductive groups proved by Bezrukavnikov, and Schneider and Stuhler. Introduction Let G0 be a connected compact Lie group. Denote by M(G0) the category of finite-dim...

Infinite-dimensional Representations of Real Reductive Groups

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...