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
Received 9 September 2002, Accepted 15 March 2006, Available Online 1 August 2006.
- DOI
- 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.
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Joseph Bernstein AU - Ossip Schwarzman PY - 2006 DA - 2006/08/01 TI - Chevalley's theorem for the complex crystallographic groups JO - Journal of Nonlinear Mathematical Physics SP - 323 EP - 351 VL - 13 IS - 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.3.2 DO - 10.2991/jnmp.2006.13.3.2 ID - Bernstein2006 ER -