Communications in Mathematical Physics

, Volume 311, Issue 1, pp 55–96

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


DOI: 10.1007/s00220-012-1424-0

Cite this article as:
Brochier, A. Commun. Math. Phys. (2012) 311: 55. doi:10.1007/s00220-012-1424-0


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 Bn 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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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.IRMA (CNRS), rue René DescartesStrasbourgFrance

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