%0 Journal Article
%T Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem
%A Robert Milson
%J Mathematics
%D 2001
%I arXiv
%X Chevalley's theorem and it's converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that in the Euclidean case, a weaker condition suffices to characterize finite reflection groups, namely that a freely-generated polynomial subring is closed with respect to the gradient product.
%U http://arxiv.org/abs/math/0111297v3