Monodromy of Fuchsian Systems on Complex Linear Spaces

On complex linear spaces, Fuchs-type Pfaffian systems are studied that are defined by configurations of vectors in these spaces. These systems are referred to as $R$-systems in this paper. For the vector configurations that are systems of roots of complex reflection groups, the monodromy representations of $R$-systems are described. These representations are deformations of the standard representations of reflection groups. Such deformations define representations of generalized braid groups corresponding to complex reflection groups and are similar to the Burau representations of the Artin braid groups.