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

@article{Brochier2010AKT,
  title={A Kohno–Drinfeld Theorem for the Monodromy of Cyclotomic KZ Connections},
  author={Adrien Brochier},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={311},
  pages={55-96}
}
  • A. Brochier
  • Published 18 November 2010
  • Mathematics
  • Communications in Mathematical Physics
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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