Analytic Bethe Ansatz and $T$-system in $C^{(1)}_2$ vertex models

TL;DR

This paper derives solutions to the $T$-system for $C^{(1)}_2$ vertex models, demonstrating compatibility with the analytic Bethe ansatz and connecting to classical characters, advancing understanding of integrable models.

Contribution

It provides the explicit solution to the $T$-system for $C^{(1)}_2$ models, linking it with the analytic Bethe ansatz and classical characters.

Findings

Solution to the $T$-system for $C^{(1)}_2$ models obtained.

Compatibility with the analytic Bethe ansatz established.

Yang-Baxterization of classical characters demonstrated.

Abstract

Eigenvalues of the commuting family of transfer matrices are expected to obey the $T$-system, a set of functional relation, proposed recently. Here we obtain the solution to the $T$-system for $C^{(1)}_2$ vertex models. They are compatible with the analytic Bethe ansatz and Yang-Baxterize the classical characters.