1997/07/10 by Benjamin Enriquez, B. Enriquez, Enriquez, B. +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9707012
Latex file, 21 pages. The new version contains a correction in the definition of evaluation representations and some improvements of the text
openalex publication_date 1997/07/10 · arxiv created 1997/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a quantum version of the construction of the KZ system of equations as a flat connection on the spaces of coinvariants of representations of tensor products of Kac-Moody algebras. We consider here representations of a tensor product of Yangian doubles and compute the coinvariants of a deformation of the subalgebra generated by the regular functions of a rational curve with marked points. We observe that Drinfeld's quantum Casimir element can be viewed as a deformation of the zero-mode of the Sugawara tensor in the Yangian double. These ingredients serve to define a compatible system of difference equations, which we identify with the quantum KZ equations introduced by I. Frenkel and N. Reshetikhin.