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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
82/2006

Complex crystallographic Coxeter groups and affine root systems

Joseph Bernstein, Dimitry A. Leites and Ossip Schwarzman

Abstract

We classify (up to an isomorphism in the category of affine groups) the complex crystallographic groups $\Gamma$ generated by reflections and such that $d\Gamma$, its linear part, is a Coxeter group, i.e., $d\Gamma$ is generated by "real" reflections of order 2.

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

Related publications

inJournal
2006 Journal Open Access
Joseph Bernstein and Ossip Schwarzman

Complex crystallographic Coxeter groups and affine root systems

In: Journal of nonlinear mathematical physics, 13 (2006) 2, pp. 163-182