Construction of determinants for the six-vertex model with domain wall boundary conditions

Abstract We consider the problem of construction determinant formulas for partition function six-vertex model with domain wall boundary conditions that depend on two sets spectral parameters. In pioneering works Korepin and Izergin a formula was proposed proved using recursion relation. later works, equivalent were given by Kostov rational case Foda Wheeler trigonometric case. Here, we develop an approach in which relation is replaced system algebraic equations respect to one prove this has unique solution. The result can be easily as parametrized arbitrary basis polynomials. particular, choice Lagrange polynomials remaining set parameters leads Izergin–Korepin representation, monomial Foda–Wheeler representations.