Bethe Ansatz for the Universal Weight Function

We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra (U) over bar (q)((gl) over cap (N)) [10, 12]. 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 [1].