Coinvariants for Yangian doubles and quantum KZ equations
Abstract
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.
Cite
@article{arxiv.q-alg/9707012,
title = {Coinvariants for Yangian doubles and quantum KZ equations},
author = {B. Enriquez and G. Felder},
journal= {arXiv preprint arXiv:q-alg/9707012},
year = {2008}
}
Comments
Latex file, 21 pages. The new version contains a correction in the definition of evaluation representations and some improvements of the text