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Invariants of Finite Reflection Groups

Published online by Cambridge University Press:  20 November 2018

Robert Steinberg
Robert Steinberg*
Affiliation:
University of California, Los Angeles
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Let us define a reflection to be a unitary transformation, other than the identity, which leaves fixed, pointwise, a (reflecting) hyperplane, that is, a subspace of deficiency 1, and a reflection group to be a group generated by reflections. Chevalley (1) (and also Coxeter (2) together with Shephard and Todd (4)) has shown that a reflection group G, acting on a space of n dimensions, possesses a set of n algebraically independent (polynomial) invariants which form a polynomial basis for the set of all invariants of G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 616 - 618
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Chevalley, C., Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778.Google Scholar
2. Coxeter, H.S.M., The product of the generators of a finite group generated by reflections, Duke Math. J., 18 (1951), 765.Google Scholar
3. Shephard, G.C., Some problems of finite reflection groups, Enseignement Math., II (1956), 42.Google Scholar
4. Shephard, G.C. and Todd, J.A., Finite unitary reflection groups, Can. J. Math., 6 (1954), 274.Google Scholar