Fusion $U_q(G^{(1)}_2)$ vertex models and analytic Bethe ans{\"a}tze

TL;DR

This paper develops fusion $U_q(G^{(1)}_2)$ vertex models and derives their transfer matrix eigenvalues using analytic Bethe ansätze, connecting these to Yangian analogues of Young tableaux and conjecturing explicit solutions.

Contribution

It introduces fusion $U_q(G^{(1)}_2)$ models, derives eigenvalues via analytic Bethe ansätze, and conjectures explicit eigenvalues using Yangian tableaux, extending previous functional relation studies.

Findings

Eigenvalues derived for fusion $U_q(G^{(1)}_2)$ models

Conjectured explicit eigenvalues for a broad class of models

Connection established with Yangian analogues of Young tableaux

Abstract

We introduce fusion $U_q(G^{(1)}_2)$ vertex models related to fundamental representations. The eigenvalues of their row to row transfer matrices are derived through analytic Bethe ans{\"a}tze. By combining these results with our previous studies on functional relations among transfer matrices(the $T$-system), we conjecture explicit eigenvalues for a wide class of fusion models. These results can be neatly expressed in terms of a Yangian analogue of the Young tableaux.