The Dynkin diagram cohomology of finite Coxeter groups

JOURNAL OF ALGEBRA

卷:323

Article

Rouquier, Raphael²  Laredo, Valerio Toledano^1,3 

[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA

[2] Univ Oxford, Math Inst, Oxford OX1 3LB, England

[3] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

关键词: Quasi-Coxeter algebras;    Dynkin diagram cohomology;    Coxeter groups;    Braid groups;    KZ connection;    Coxeter complex;   

DOI  :  10.1016/j.jalgebra.2009.09.023

来源: Elsevier

【 摘 要 】

Let D be a connected graph. The Dynkin complex CD(A) of a D-algebra A was introduced by the second author to control the deformations of quasi-Coxeter algebra structures on A. In the present paper, we study the cohomology of this complex when A is the group algebra of a Coxeter group W and D is the Dynkin diagram of W. We compute this cohomology when W is finite and prove in particular the rigidity of quasi-Coxeter algebra structures on kW. For an arbitrary W. we compute the top cohomology group and obtain a number of additional partial results when W is affine. Our computations are carried out by filtering the Dynkin complex by the number of vertices of subgraphs of D. The corresponding graded complex turns out to be dual to the sum of the Coxeter complexes of all standard, irreducible parabolic subgroups of W. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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