Flat connections and Brauer Type Algebras · arXivDesk
1102.4389Feb 22, 2011This paper is an improved version of my last one "Algebras associated with Pseudo Reflection Groups: A Generalization of Brauer Algebras", with many mistakes corrected and new contents added
We introduce a Brauer type algebra BG(Υ) associated with every pseudo reflection group and every Coxeter group G. When G is a Coxeter group of simply-laced type we show BG(Υ)
Nearby in the stack
is isomorphic to the generalized Brauer algebra of simply-laced type introduced by Cohen, Gijsbers and Wales ( J. Algebra, 280 (2005), 107-153). We also prove
BG(Υ)
has a cellular structure and be semisimple for generic parameters when
G
is a dihedral group or the type
H3
Coxeter group. Moreover, in the process of construction, we introduce a further generalization of Lawrence-Krammer representation to complex braid groups associated with all pseudo reflection groups.