Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy

TL;DR

This paper develops a mathematical framework for analyzing interaction-round-a-face models with fixed boundary conditions, using boundary weights and reflection equations to derive commuting transfer matrices and explore their algebraic structure.

Contribution

It introduces a fusion hierarchy for ABF models with fixed boundaries, revealing functional equations with an su(2) structure for the transfer matrices.

Findings

Derived families of commuting double-row transfer matrices.

Established functional equations with su(2) symmetry.

Extended the fusion hierarchy for ABF models.

Abstract

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester models, for which we find that the double-row transfer matrices satisfy functional equations with an su(2) structure.