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A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections (1011.4285v1)

Published 18 Nov 2010 in math.QA and math.RT

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 $B_n1$. 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 $B_n1$ using dynamical twists. Then, we show how these "algebraic" representations may be identified with the above "analytic" monodromy representations.

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