# On higher dimensional analogues of braid representations.

Given a complex semisimple Lie algebra and representations of it, the Khono-Drinfeld construction produces representations of the braid group $B_n$, which is the fundamental group of the configuration space of points in the plane.
In this talk we will discuss a higher dimensional analogue of this construction that arises from flat connections in the configuration spaces of points in $\mathbb{R}^n$.