Diagonal $K$-matrices and transfer matrix eigenspectra associated with the $G^{(1)}_2$ $R$-matrix

TL;DR

This paper classifies all diagonal K-matrices for the G^{(1)}_2 R-matrix, diagonalizes the transfer matrices using an analytic Bethe ansatz, and compares results with the A^{(2)}_2 case.

Contribution

It provides a complete classification of diagonal K-matrices for the G^{(1)}_2 R-matrix and applies an analytic Bethe ansatz to diagonalize the transfer matrices.

Findings

Complete set of diagonal K-matrices identified.

Transfer matrices successfully diagonalized.

Notable similarities with A^{(2)}_2 case observed.

Abstract

We find all the diagonal $K$-matrices for the $R$-matrix associated with the minimal representation of the exceptional affine algebra $G^{(1)}_2$. The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe ansatz. We find many similarities with the case of the Izergin-Korepin $R$-matrix associated with the affine algebra $A^{(2)}_2$.