Flat connections and Brauer type algebras

In this paper, 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 that BG(ϒ) is isomorphic to the generalized Brauer algebra of simply-laced type introduced by Cohen, Gijsbers, and Wales (2005) [CGW1]. We also prove that 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 the Lawrence–Krammer representation to complex braid groups associated with all pseudo reflection groups.