## Asymptotic $K$-support and restrictions of representations

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- by Sönke Hansen, Joachim Hilgert and Sameh Keliny PDF
- Represent. Theory
**13**(2009), 460-469 Request permission

## 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.## References

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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
- Received by editor(s): May 4, 2009
- Received by editor(s) in revised form: August 25, 2009
- Published electronically: September 25, 2009
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**13**(2009), 460-469 - MSC (2000): Primary 22E46; Secondary 46F10
- DOI: https://doi.org/10.1090/S1088-4165-09-00362-8
- MathSciNet review: 2550473