A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)

TL;DR

This paper computes a universal weight function, also known as off-shell Bethe vectors, for the quantum affine algebra U_q(\hat{rak{gl}}_N) using projection methods of Drinfeld currents, applicable in any representation with a weight singular vector.

Contribution

It introduces a method to explicitly compute off-shell Bethe vectors for U_q(\hat{rak{gl}}_N) using projections of Drinfeld currents, extending previous approaches.

Findings

Explicit formula for the universal weight function derived.

Applicable to any representation with a weight singular vector.

Advances the understanding of quantum affine algebra representations.

Abstract

We compute an universal weight function (off-shell Bethe vectors) in any representation with a weight singular vector of the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_N)$ applying the method of projections of Drinfeld currents developed in arXiv:math/0610398.