# A Kohno–Drinfeld Theorem for the Monodromy of Cyclotomic KZ Connections

@article{Brochier2010AKT, title={A Kohno–Drinfeld Theorem for the Monodromy of Cyclotomic KZ Connections}, author={Adrien Brochier}, journal={Communications in Mathematical Physics}, year={2010}, volume={311}, pages={55-96} }

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 Bn 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.

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