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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
83/2006

Chevalley's theorem for the complex crystallographic groups

Joseph Bernstein, Dimitry A. Leites and Ossip Schwarzman

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.

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

Related publications

inJournal
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