Journal of Nonlinear Mathematical Physics

Volume 13, Issue 3, August 2006, Pages 323 - 351

Chevalley's theorem for the complex crystallographic groups

Authors
Joseph BERNSTEIN, Ossip SCHWARZMAN
Corresponding Author
Joseph BERNSTEIN
Available Online 9 November 2006.
DOI
https://doi.org/10.2991/jnmp.2006.13.3.2How to use a DOI?
Keywords
crystallographic, Coxeter, topological conformal field theory
Abstract
We prove that, for the irreducible complex crystallographic Coxeter 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. We also discuss the status of the above statement for other types of complex crystallographic group W and certain generalizations of the statement. It is impossible to read this paper without first reading our paper [5] which contains all the notations and the data on affine root systems and complex crystallographic Coxeter groups. All the data needed on the modular functions theory is collected in §4.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 3
Pages
323 - 351
Publication Date
2006/11
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2006.13.3.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Joseph BERNSTEIN
AU  - Ossip SCHWARZMAN
PY  - 2006
DA  - 2006/11
TI  - Chevalley's theorem for the complex crystallographic groups
JO  - Journal of Nonlinear Mathematical Physics
SP  - 323
EP  - 351
VL  - 13
IS  - 3
SN  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2006.13.3.2
DO  - https://doi.org/10.2991/jnmp.2006.13.3.2
ID  - BERNSTEIN2006
ER  -