nLab
Drinfeld-Kohno theorem

Contents

Contents

Idea

The Drinfel’d-Kohno theorem is about a geometric relation between classical and quantum RR-matrices for quantum groups: the monodromies of the solutions of Knizhnik-Zamolodchikov equations (which are equations of Fuchsian type) for a given classical rr-matrix give rise to the corresponding quantum RR-matrix; more precisely it gives the same representation of the braid group.

References

  • Toshitake Kohno, Monodromy representations of braid groups and Yang-Baxter equations, Annales de l’institut Fourier 37, no. 4 (1987), p. 139-160, numdam

  • Toshitake Kohno, Conformal field theory and topology, transl. from the 1998 Japanese original by the author. Translations of Mathematical Monographs 210. Iwanami Series in Modern Mathematics. Amer. Math. Soc. 2002. x+172 pp.

  • P. Etingof, O. Shiffman, Lectures on quantum groups

  • P. Etingof, N. Geer, Monodromy of trigonometric KZ equations, math.QA/0611003

  • Valerio Toledano-Laredo, A Kohno-Drinfeld theorem for quantum Weyl groups, math.QA/0009181

  • V. Chari, A. Pressley, A guide to quantum groups, 1994

  • Uli Kraehmer, Knizhnik-Zamolodchikov and Drinfeld-Kohno, slides, pdf

  • C. Kassel, Quantum groups, Springer 1995

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