Intertwining operators for real reductive groups

Functional Equations Satisfied by Intertwining Operators of Reductive Groups

This paper generalizes a recent work of Vogan and Wallach [VW] in which they derived a difference equation satisfied by intertwining operators of reductive groups. We show that, associated with each irreducible finitedimensional representation, there is a functional equation relating intertwining operators. In this way, we obtain natural relations between intertwining operators for different se...

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...

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.

Intertwining Operators and Residues

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...