Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem

Robert Milson

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Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem

Robert Milson

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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.

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Robert Milson. 2002-09-05. Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem. https://arxiv.org/abs/math/0111297

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