Monodromy of Veselov-Kohno-Cherednik R-systems
The paper studies Pfaffian systems of the Fuchs type on complex linear spaces defined by configurations of vectors in these spaces. It is shown that the Veselov ∨-condition imposed on a configuration of vectors is equivalent to the integrability of these system. For configuration of vectors that are root systems, a description of monodromy representations of the Pfaffian systems considered is given. These representations are deformations of the standard representations of reflection groups of the Burau type and were defined earlier by Squier and Givental’.
KeywordsRoot System Group Algebra Braid Group Coxeter Group Cartan Matrix
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