Reflection equations and exactly solvable lattice spin models

Abstract

Reflection equations are used to obtain families of commuting double-row transfer matrices for interaction-round-a-face (IRF) models with fixed and free boundary conditions. We illustrate our methods for the Andrews-Baxter-Forrester (ABF) models which areL-state models associated with the quantum groupU q (su(2)) at a root of unity. We construct elliptic solutions to the reflection equations for the ABF models by a procedure which uses fusion to build the solutions starting from a trivial solution. Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.