Mathematics – Quantum Algebra
Scientific paper
1997-05-26
Mathematics
Quantum Algebra
20 pages
Scientific paper
The elliptic quantum Knizhnik-Zamolodchikov-Bernard (qKZB) difference equations associated to the elliptic quantum group $E_{\tau,\eta}(sl_2)$ is a system of difference equations with values in a tensor product of representations of the quantum group and defined in terms of the elliptic R-matrices associated with pairs of representations of the quantum group. In this paper we solve the qKZB equations in terms of elliptic hypergeometric functions and decribe the monodromy properties of solutions. It turns out that the monodromy transformations of solutions are described in terms of elliptic R-matrices associated with pairs of representations of the "dual" elliptic quantum group $E_{p,\eta}(sl_2)$, where $p$ is the step of the difference equations. Our description of the monodromy is analogous to the Kohno-Drinfeld description the monodromy group of solutions of the KZ differential equations associated to a simple Lie algebra in terms of the corresponding quantum group.
Felder Giovanni
Tarasov Vitaly
Varchenko Alexander
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