Title

Wave front sets of reductive lie group representations

Document Type

Article

Publication Date

4-1-2016

Abstract

If G is a Lie group, H ⊂ G is a closed subgroup, and τ is a unitary representation of H, then the authors give a sufficient condition on ξ ε ig* to be in the wave front set of IndGH τ. In the special case where τ is the trivial representation, this result was conjectured by Howe. If G is a real, reductive algebraic group and π is a unitary representation of G that is weakly contained in the regular representation, then the authors give a geometric description of WF(π) in terms of the direct integral decomposition of π into irreducibles. Special cases of this result were previously obtained by Kashiwara-Vergne, Howe, and Rossmann. The authors give applications to harmonic analysis problems and branching problems.

Publication Source (Journal or Book title)

Duke Mathematical Journal

First Page

793

Last Page

846

This document is currently not available here.

Share

COinS