A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections

Adrien Brochier

paper

A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections

arXiv:1011.4285

Abstract

We compute explicitly the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_{n}^{1}$ . We show how the representations of the braid group $B_{n}$ obtained using quantum groups and universal $R$ -matrices may be enhanced to representations of $B_{n}^{1}$ using dynamical twists. Then, we show how these "algebraic" representations may be identified with the above "analytic" monodromy representations.