Bethe Ansatz for the Universal Weight Function

TL;DR

This paper studies the properties of universal off-shell Bethe vectors within the quantum affine algebra framework, establishing their eigenvector status under certain conditions related to the Bethe equations.

Contribution

It provides a detailed analysis of the ordering properties and eigenvector conditions of universal off-shell Bethe vectors in $U_q(\widehat{gl}_N)$.

Findings

Bethe vectors are eigenvectors of the transfer matrix when Bethe parameters satisfy universal Bethe equations.

Derived ordering properties of the product of transfer matrix and Bethe vectors.

Established conditions under which off-shell Bethe vectors become eigenvectors.

Abstract

We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q(\widehat{gl}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the product of the transfer matrix and these vectors. We derive that these vectors are eigenvectors of the transfer matrix if their Bethe parameters satisfy the universal Bethe equations [arXiv:math-ph/0512037].