Rigidity in the invariant theory of compact groups
Representation Theory
2007-05-23 v1 Group Theory
Abstract
A compact Lie group G and a faithful complex representation V determine a Sato-Tate measure, defined as the direct image of Haar measure on G with respect to the character of V. We give a necessary and sufficient condition for a Sato-Tate measure to be an isolated point in the set of such measures, regarded as a subset of the space of distributions. In particular we prove that the Sato-Tate measure of a connected and semisimple group with respect to an irreducible representation is an isolated point.
Cite
@article{arxiv.math/0212193,
title = {Rigidity in the invariant theory of compact groups},
author = {Michael J. Larsen},
journal= {arXiv preprint arXiv:math/0212193},
year = {2007}
}
Comments
11 pages