Diagonal $K$-matrices and transfer matrix eigenspectra associated with the $G_2^{(1)}$ $R$-matrix

Abstract

We find all the diagonal $K$-matrices for the $R$-matrix associated with the minimal representation of the exceptional affine algebra $G_2^{(1)}$. 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 $A_2^{(2)}$.

11 pages, LaTeX

References in corpus (6)

• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Exact Bethe Ansatz solution for $A_{n-1}$ chains with non-$S{U}_q(n)$ invariant open boundary conditions
• Fusion $U_q(G_2^{(1)})$ vertex models and analytic Bethe ans{ä}tze

Cited by in corpus (11)

• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Analytical Bethe Ansatz for $A_{2n-1}^{(2)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ quantum-algebra-invariant open spin chains
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Integrable O(n) model on the honeycomb lattice via reflection matrices : Surface critical behaviour
• Surveying the quantum group symmetries of integrable open spin chains
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• The spectrum of quantum-group-invariant transfer matrices
• The spectrum properties of an integrable $G_2$ invariant vertex model
• Exact solution of a quantum integrable system associated with the $G_2$ exceptional Lie algebra
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries