An Izergin–Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices

Abstract

We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin–Korepin formula for the six-vertex model. As applications, we find dynamical (in the sense of the dynamical Yang–Baxter equation) generalizations of the enumeration and 2-enumeration of alternating sign matrices. The dynamical enumeration has a nice interpretation in terms of three-colourings of the square lattice.