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Reflection quotients in Riemannian geometry. A geometric converse to Chevalley's theorem

Author: R. Milson
Journal: Proc. Amer. Math. Soc. 132 (2004), 2825-2831
MSC (2000): Primary 20H15, 14L24, 53B21
Published electronically: June 2, 2004
MathSciNet review: 2063099
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Abstract: Chevalley's theorem and its 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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Additional Information

R. Milson
Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Keywords: Reflection groups, invariants, degenerate metrics
Received by editor(s): December 3, 2001
Received by editor(s) in revised form: June 12, 2002
Published electronically: June 2, 2004
Additional Notes: The author was supported by NSERC grant 228057
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2004 American Mathematical Society

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