The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules

arXivq-alg/9709026MaRDI QIDQ6502366

Evgenii E. Mukhin, Alexander Varchenko

Abstract: We consider the quantized Knizhnik-Zamolodchikov difference equation (qKZ) with values in a tensor product of irreducible sl(2) modules, the equation defined in terms of rational R-matrices. We solve the equation in terms of multidimensional q-hypergeometric integrals. We identify the space of solutions of the qKZ equation with the tensor product of the corresponding modules over the quantum group $U_{q}sl(2)$. We compute the monodromy of the qKZ equation in terms of the trigonometric R-matrices.

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