Free Field Approach to Solutions of the Quantum Knizhnik–Zamolodchikov Equations

Solutions of the qKZ equation associated with the quantum affine algebra $U_q(\widehat{sl}_2)$ and its two dimensional evaluation representation are studied. The integral formulae derived from the free field realization of intertwining operators of $q$-Wakimoto modules are shown to coincide with those of Tarasov and Varchenko.