Fusion hierarchies, T-systems and Y-systems for the models

Abstract

Listen

Translate article

The family of models on the square lattice includes a dilute loop model, a -vertex model and, at roots of unity, a family of RSOS models. The fused transfer matrices of the general loop and vertex models are shown to satisfy -type fusion hierarchies. We use these to derive explicit - and -systems of functional equations. At roots of unity, we further derive closure identities for the functional relations and show that the universal -system closes finitely. The RSOS models are shown to satisfy the same functional and closure identities but with finite truncation.