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

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

2010-11-18

arxiv.org/abs/1011.4285v1

Mathematics

Quantum Algebra

Scientific paper

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.

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