The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

2014/11/11 by Garbali, Alexander
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1411.2903

Abstract

We study the domain wall partition function Z_N for the U_q(A₂⁽²⁾) (Izergin-Korepin) integrable 19-vertex model on a square lattice of size N. Z_N is a symmetric function of two sets of parameters: horizontal ζ₁,..,ζ_N and vertical z₁,..,z_N rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition function relating Z_N+1 to P_N Z_N, where P_N is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables ζ₁,..,ζ_N and z₁,..,z_N. After setting q³=-1 the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by P_N.

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