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arXiv · 1809.07868

Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models

Alexi Morin-Duchesne·Paul A. Pearce·Jorgen Rasmussen
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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 $s\ell(3)$-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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Alexi Morin-Duchesne, Paul A. Pearce, Jorgen Rasmussen. 2018-09-20. Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models. https://doi.org/10.1088/1742-5468%2Faaf632

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