A Kohno-Drinfeld theorem for cyclotomic KZ connections

Adrien Brochier (U Edinburgh)

Wednesday 16th January, 2013 16:00-17:00 516

Abstract

The aim of this talk is to give an explicit computation of 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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