Fusion hierarchies, T-systems and Y-systems for the $A_2^{(1)}$ models
(2019) J. Stat. Mech. Theory Exp. — p. 13101 (2019)
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- Abstract
- The family of $A^{(1)}_2$ models on the square lattice includes a dilute loop model, a $15$-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 $sl(3)$-type fusion hierarchies. We use these to derive explicit $T$- and $Y$-systems of functional equations. At roots of unity, we further derive closure identities for the functional relations and show that the universal $Y$-system closes finitely. The $A^{(1)}_2$ RSOS models are shown to satisfy the same functional and closure identities but with finite truncation.
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Morin Duchesne, A., Pearce, P., & Rasmussen, J. (2019). Fusion hierarchies, T-systems and Y-systems for the $A_2^{(1)}$ models. J. Stat. Mech. Theory Exp., 13101. https://hdl.handle.net/2078.5/93741 (Original work published 2019)