SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl2 dKZ EQUATION WITH LEVEL −4

Abstract

A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.