Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group $E_{τ,η}sl_2$

Details Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group $E_{τ,η}sl_2$ Solutions of the qKZB Equation in Tensor Products of finite dimensional modules over the elliptic quantum group $E_{τ,η}sl_2$

1997-12-26

arxiv.org/abs/q-alg/9712056v1

Mathematics

Quantum Algebra

Latex, 11 pages

Scientific paper

We consider the quantized Knizhnik-Zamolodchikov-Bernard difference equation (qKZB) with step $p$ and values in a tensor product of finite dimensional evaluation modules over the elliptic quantum group $E_{\tau,\eta}(sl_2)$, the equation defined in terms of elliptic dynamical R-matrices. We solve the equation in terms of multidimensional q-hypergeometric integrals and describe its monodromy properties. We identify the space of solutions of the qKZ equation with the space of functions with values in the tensor product of the corresponding modules over the elliptic quantum group $E_{p,\eta}(sl_2)$.

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