Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20H15, 14L24, 53B21

Retrieve articles in all journals with MSC (2000): 20H15, 14L24, 53B21


Additional Information

R. Milson
Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email: milson@mscs.dal.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07583-5
PII: S 0002-9939(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