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

DOI:
https://doi.org/10.1090/S0002-9939-04-07583-5

Published electronically:
June 2, 2004

MathSciNet review:
2063099

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Abstract | References | Similar Articles | Additional Information

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

Email:
milson@mscs.dal.ca

DOI:
https://doi.org/10.1090/S0002-9939-04-07583-5

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