nLab
Drinfeld-Kohno theorem

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

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