Degenerate Whittaker functionals for real reductive groups

TL;DR

This paper links the associated variety of representations of quasi-split real reductive groups to the existence of degenerate Whittaker functionals, extending previous results to a broader class of groups and vectors.

Contribution

It generalizes the connection between associated varieties and Whittaker functionals to all quasi-split real reductive groups for both smooth and K-finite vectors.

Findings

Established the connection for all quasi-split real reductive groups.

Extended previous results to include degenerate Whittaker functionals.

Applicable to both smooth and K-finite vectors.

Abstract

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.