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Flat connections and Brauer Type Algebras
We introduce a Brauer type algebra associated with every
pseudo reflection group and every Coxeter group . When is a Coxeter
group of simply-laced type we show is isomorphic to the
generalized Brauer algebra of simply-laced type introduced by Cohen, Gijsbers
and Wales ({\it J. Algebra}, {\bf 280} (2005), 107-153). We also prove has a cellular structure and be semisimple for generic parameters
when is a dihedral group or the type 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.Comment: This 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 adde
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