2006/10/31 by Pavel Etingof, Etingof, Pavel, Nathan Geer +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.math/0611003
The famous Drinfeld-Kohno theorem for simple Lie algebras states that the monodromy representation of the Knizhnik-Zamolodchikov equations for these Lie algebras expresses explicitly via R-matrices of the corresponding Drinfeld-Jimbo quantum groups. This result was generalized by the second author to simple Lie superalgebras of type A-G. In this paper, we generalize the Drinfeld-Kohno theorem to the case of the trigonometric Knizhnik-Zamolodchikov equations for simple Lie superalgebras of type A-G. The equations contain a classical r-matrix on the Lie superalgebra, and the answer expresses through the quantum R-matrix of the corresponding quantum group. The proof is based on the quantization theory for Lie bialgebras developed by the first author and D. Kazhdan.