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

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