Flat connections and Brauer type algebras

JOURNAL OF ALGEBRA

卷:365

Article

Chen, Zhi

关键词: Brauer algebras;    BMW algebras;    Coxeter groups;    Braid groups;    KZ equations;   

DOI  :  10.1016/j.jalgebra.2012.04.022

来源: Elsevier

【 摘 要 】

In this paper, we introduce a Brauer type algebra B-G(gamma) associated with every pseudo reflection group and every Coxeter group G. When G is a Coxeter group of simply-laced type we show that B-G(gamma) is isomorphic to the generalized Brauer algebra of simply-laced type introduced by Cohen, Gijsbers, and Wales (2005) [CGW1]. We also prove that B-G(gamma) has a cellular structure and be semisimple for generic parameters when G is a dihedral group or the type H-3 Coxeter group. Moreover, in the process of construction, we introduce a further generalization of the Lawrence-Krammer representation to complex braid groups associated with all pseudo reflection groups. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free