Rigidity in the invariant theory of compact groups

Details Rigidity in the invariant theory of compact groups Rigidity in the invariant theory of compact groups

2002-12-15

arxiv.org/abs/math/0212193v1

Mathematics

Representation Theory

11 pages

Scientific paper

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.

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