Smirnov's Integrals and Quantum Knizhnik-Zamolodchikov Equation of Level $0$

Abstract

We study the quantum Knizhnik-Zamolodchikov equation of level $0$ associated with the spin $1/2$ representation of $U_q\left(\widehat{\mathfrak{s}{\mathfrak{l}}_2}\right)$. We find an integral formula for solutions in the case of an arbitrary total spin and $|q|<1$. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed.

19 pages