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
Recommended Citation
Harris, B., He, H., & Ólafsson, G. (2016). Wave front sets of reductive lie group representations. Duke Mathematical Journal, 165 (5), 793-846. https://doi.org/10.1215/00127094-3167168
