Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras

TL;DR

This paper develops functional relations for transfer matrices in solvable models linked to twisted quantum affine algebras and derives their solutions using the analytic Bethe ansatz, advancing understanding of these algebraic structures.

Contribution

It introduces new functional relations for transfer matrices of twisted quantum affine algebras and provides their solutions via the analytic Bethe ansatz, including conjectures for certain cases.

Findings

Solutions obtained for $A^{(2)}_n$ models.

Conjectured solutions for $D^{(3)}_4$ models.

Enhanced understanding of transfer matrices in twisted quantum affine algebras.

Abstract

Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras $U_q(X^{(\kappa)}_n)$ where $X^{(\kappa)}_n = A^{(2)}_n, D^{(2)}_n, E^{(2)}_6$ and $D^{(3)}_4$. Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.