Reflection quotients in Riemannian geometry. A geometric converse to Chevalley’s theorem
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- by R. Milson PDF
- Proc. Amer. Math. Soc. 132 (2004), 2825-2831 Request permission
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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2063099