Solutions of the sl2${\mathfrak {sl}_2}$qKZ equations modulo an integer

Abstract

AbstractWe study the qKZ difference equations with values in the th tensor power of the vector representation , variables , and integer step . For any integer relatively prime to the step , we construct a family of polynomials in variables with values in such that the coordinates of these polynomials with respect to the standard basis of are polynomials with integer coefficients. We show that satisfy the qKZ equations modulo . Polynomials are modulo analogs of the hypergeometric solutions of the qKZ given in the form of multidimensional Barnes integrals.