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Coinvariants for Yangian doubles and quantum KZ equations

B. Enriquez·G. Felder
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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.

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BibTeXRIS

B. Enriquez, G. Felder. 1997-07-15. Coinvariants for Yangian doubles and quantum KZ equations. https://arxiv.org/abs/q-alg/9707012

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