Wave front sets of reductive lie group representations
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
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