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Asymptotic $ K$-support and restrictions of representations


Authors: Sönke Hansen, Joachim Hilgert and Sameh Keliny
Journal: Represent. Theory 13 (2009), 460-469
MSC (2000): Primary 22E46; Secondary 46F10
DOI: https://doi.org/10.1090/S1088-4165-09-00362-8
Published electronically: September 25, 2009
MathSciNet review: 2550473
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Abstract: The restriction, from a compact Lie group $ K$ to a closed subgroup, of a polynomially bounded representation remains polynomially bounded provided a geometric assumption on the asymptotic $ K$-support of the representation is satisfied. This is a theorem of T. Kobayashi. We give a proof of this theorem using microlocal analysis in the setting of distribution rather than hyperfunction theory. The proof is based on a characterization, up to the natural $ K\times K$ action, of the wavefront set of a distribution on $ K$ in terms of the asymptotic behavior of its Fourier coefficients.


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Additional Information

Sönke Hansen
Affiliation: Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
Email: soenke@math.upb.de

Joachim Hilgert
Affiliation: Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
Email: hilgert@math.upb.de

Sameh Keliny
Affiliation: Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
Email: sameh@math.upb.de

DOI: https://doi.org/10.1090/S1088-4165-09-00362-8
Received by editor(s): May 4, 2009
Received by editor(s) in revised form: August 25, 2009
Published electronically: September 25, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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