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MiS Preprint

Chevalley's theorem for the complex crystallographic groups

Joseph Bernstein, Dimitry A. Leites and Ossip Schwarzman


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.

Aug 22, 2006
Aug 22, 2006
MSC Codes:
32B30, 20H15, 32C40
Coxeter groups, invariant theory

Related publications

2006 Journal Open Access
Joseph Bernstein and Ossip Schwarzman

Chevalley's theorem for the complex crystallographic groups

In: Journal of nonlinear mathematical physics, 13 (2006) 3, pp. 323-351