  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.
