A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

TL;DR

This paper introduces a method to generate new solutions to reflection equations in interaction-round-a-face lattice models, especially for models with a fusion hierarchy and specific graph structures, exemplified by the Andrews-Baxter-Forrester models.

Contribution

The paper develops a novel procedure to construct reflection equation solutions using known solutions, applicable to models with fusion hierarchies and certain graph configurations.

Findings

Constructed reflection solutions for Andrews-Baxter-Forrester models

Applicable to models with a node of valency 1 in their graph

Provides solutions for fixed and free boundary conditions

Abstract

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.