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

Adrien Brochier*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 B1 n. We show how the representations of the braid group Bn obtained using quantum groups and universal R- matrices may be enhanced to representations of B1 n using dynamical twists. Then, we show how these " algebraic" representations may be identified with the above " analytic" monodromy representations.

Original languageEnglish
Pages (from-to)55-96
Number of pages42
JournalCommunications in Mathematical Physics
Volume311
Issue number1
DOIs
Publication statusPublished - Apr 2012

Keywords

  • ALGEBRAS
  • NONABELIAN BASE
  • YANG-BAXTER EQUATIONS
  • DYNAMICAL R-MATRICES
  • BRAID-GROUPS
  • QUANTIZATION

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