The domain wall partition function for the Izergin-Korepin nineteen-vertex model at a root of unity

Abstract

We study the domain wall partition function Z N for the (Izergin-Korepin) integrable nineteen-vertex model on a square lattice of size N. Z N is a symmetric function of two sets of parameters: horizontal and vertical rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition function relating Z N+1 to , where P N is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables and . After setting the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by P N.