q-Wakimoto Modules and Integral Formulae of the Quantum Knizhnik-Zamolodchikov Equations

TL;DR

This paper demonstrates that matrix elements of intertwining operators between q-Wakimoto modules match Tarasov-Varchenko's solutions to the quantum Knizhnik-Zamolodchikov equations, generalizing previous results for arbitrary spins.

Contribution

It establishes a connection between intertwining operator matrix elements and integral formulae for qKZ solutions in the context of arbitrary spin representations.

Findings

Matrix elements coincide with Tarasov-Varchenko's formulae

Generalization to arbitrary spins

Extends previous results to broader representation classes

Abstract

Matrix elements of intertwining operators between $q$-Wakimoto modules associated to the tensor product of representations of $U_q(\widehat{sl_2})$ with arbitrary spins are studied. It is shown that they coincide with the Tarasov-Varchenko's formulae of the solutions of the qKZ equations. The result generalizes that of the previous paper [Kuroki K., Nakayashiki A., SIGMA 4 (2008), 049, 13 pages, arXiv:0802.1776].