Asymptotic -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 to a closed subgroup, of a polynomially bounded representation remains polynomially bounded provided a geometric assumption on the asymptotic -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 action, of the wavefront set of a distribution on 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.