English

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.

Keywords

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

R2 v1 2026-07-22T16:50:17.129Z