Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem
Differential Geometry
2007-05-23 v3 Group Theory
Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.math/0111297,
title = {Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem},
author = {Robert Milson},
journal= {arXiv preprint arXiv:math/0111297},
year = {2007}
}