TY - JOUR

T1 - Chevalley's theorem for the complex crystallographic groups

AU - Bernstein, Joseph

AU - Schwarzman, Ossip

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33748438398&partnerID=8YFLogxK

U2 - 10.2991/jnmp.2006.13.3.2

DO - 10.2991/jnmp.2006.13.3.2

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AN - SCOPUS:33748438398

SN - 1402-9251

VL - 13

SP - 323

EP - 351

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 3

ER -