Chevalley's theorem for the complex crystallographic groups

Joseph Bernstein, Dimitry A. Leites, and Ossip Schwarzman

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Submission date: 22. Aug. 2006 (revised version: August 2006)
Pages: 32
published in: Journal of nonlinear mathematical physics, 13 (2006) 3, p. 323-351 
DOI number (of the published article): 10.2991/jnmp.2006.13.3.2
Bibtex
MSC-Numbers: 32B30, 20H15, 32C40
Keywords and phrases: Coxeter groups, invariant theory
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Abstract:
We prove that for the irreducible Coxeter complex crystallographic group W the following conditions are equivalent:
a) W is generated by reflections;
b) the analytic variety X/W is isomorphic to a weighted projective space.
The result is of interest, for example, in application to topological conformal field theory.