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

TL;DR

This paper derives a new formula for the 8VSOS model's partition function, extending the Izergin-Korepin formula, and applies it to enumerate alternating sign matrices with dynamical generalizations.

Contribution

It introduces a novel Izergin-Korepin-type identity for the 8VSOS model's partition function, enabling new dynamical enumeration methods for alternating sign matrices.

Findings

New expression for 8VSOS partition function

Dynamical enumeration of alternating sign matrices

Interpretation via three-colourings of the lattice

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.