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Transactions of the American Mathematical Society

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Wave front sets of reductive Lie group representations II


Author: Benjamin Harris
Journal: Trans. Amer. Math. Soc. 370 (2018), 5931-5962
MSC (2010): Primary 22E46, 22E45, 43A85
DOI: https://doi.org/10.1090/tran/7282
Published electronically: November 30, 2017
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Abstract: In this paper it is shown that the wave front set of a direct integral of singular, irreducible representations of a real, reductive algebraic group is contained in the singular set. Combining this result with the results of the first paper in this series, the author obtains asymptotic results on the occurrence of tempered representations in induction and restriction problems for real, reductive algebraic groups.


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Additional Information

Benjamin Harris
Affiliation: Department of Mathematics, Bard College at Simon’s Rock, Great Barrington, Massachusetts 01230
Email: Benjamin.Harris@simons-rock.edu

DOI: https://doi.org/10.1090/tran/7282
Keywords: Wave front set, singular spectrum, analytic wave front set, reductive Lie group, real reductive algebraic group, induced representation, tempered representation, branching problem, discrete series, reductive homogeneous space
Received by editor(s): January 16, 2015
Received by editor(s) in revised form: March 26, 2017
Published electronically: November 30, 2017
Additional Notes: The author was an NSF VIGRE postdoc at Louisiana State University while this research was conducted.
Article copyright: © Copyright 2017 American Mathematical Society

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