Algebras associated with Pseudo Reflection Groups: A Generalization of Brauer Algebras

2010/03/27 by Zhi Chen, Chen, Zhi
Mathematics · #20C08 #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1003.5280

openalex publication_date 2010/03/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a way to associate an algebra B_G (Υ) with every pseudo reflection group G. When G is a Coxeter group of simply-laced type we show B_G (Υ) is isomorphic to the generalized Brauer algebra of simply-laced type introduced by Cohen,Gijsbers and Wales[10]. We prove B_G (Υ) has a cellular structure and be semisimple for generic parameters when G is a rank 2 Coxeter group. In the process of construction we introduce a Cherednik type connection for BMW algebras and a generalization of Lawrence-Krammer representation to complex braid groups associated with all pseudo reflection groups.

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