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- Title
Asymptotic $K$-support and restrictions of representations.
- Authors
Sönke Hansen; Joachim Hilgert; Sameh Keliny
- 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 $Ktimes K$ action, of the wavefront set of a distribution on $K$ in terms of the asymptotic behavior of its Fourier coefficients.
- Subjects
REPRESENTATIONS of lie groups; COMPACT groups; MATHEMATICAL proofs; MICROLOCAL analysis; HYPERFUNCTIONS; FOURIER analysis; GEOMETRIC analysis; DISTRIBUTION (Probability theory)
- Publication
Representation Theory, 2009, Vol 13, Issue 21, p460
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/S1088-4165-09-00362-8