2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142479We 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/0610398.40 pages, typos corrected, reference addedQuantum AlgebraHigh Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable Systems17B37; 16W30; 81R50; 82B23text