Reduced invariant sets
Representation Theory
2011-09-19 v1 Group Theory
Abstract
Let K be a compact Lie group and W a finite-dimensional real K-module. Let X be a K-stable real algebraic subset of W. Let I(X) denote the ideal of X in R[W] and let I_K(X) be the ideal generated by I(X)^K. We find necessary conditions and sufficient conditions for I(X)= I_K(X) and for \sqrt{I_K(X)}=I(X). We consider analogous questions for actions of complex reductive groups.
Cite
@article{arxiv.1109.3646,
title = {Reduced invariant sets},
author = {Gerald W. Schwarz},
journal= {arXiv preprint arXiv:1109.3646},
year = {2011}
}
Comments
To appear in Journal of Fixed Point Theory and Applications