1 April 2016 Wave front sets of reductive Lie group representations
Benjamin Harris, Hongyu He, Gestur Ólafsson
Duke Math. J. 165(5): 793-846 (1 April 2016). DOI: 10.1215/00127094-3167168


If G is a Lie group, HG is a closed subgroup, and τ is a unitary representation of H, then the authors give a sufficient condition on ξig to be in the wave front set of IndHGτ. 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.


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Benjamin Harris. Hongyu He. Gestur Ólafsson. "Wave front sets of reductive Lie group representations." Duke Math. J. 165 (5) 793 - 846, 1 April 2016. https://doi.org/10.1215/00127094-3167168


Received: 9 November 2013; Revised: 24 March 2015; Published: 1 April 2016
First available in Project Euclid: 14 January 2016

zbMATH: 1341.22008
MathSciNet: MR3482333
Digital Object Identifier: 10.1215/00127094-3167168

Primary: 22E46
Secondary: 22E45 , 43A85

Keywords: analytic wave front set , branching problem , discrete series , induced representation , reductive homogeneous space , reductive Lie group , singular spectrum , tempered representation , wave front set

Rights: Copyright © 2016 Duke University Press


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Vol.165 • No. 5 • 1 April 2016
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