Abstract
The projections of the product of the Drinfeld’s currents onto intersections of the different Borel subalgebras in the current realization of the quantum affine algebra \(U_{q} {\left({\widehat{{{\mathfrak{g}}{\mathfrak{l}}}}}_{N}\right)}\) are calculated. It was shown that this projections has the structure of the off-shell nested Bethe ansatz vectors.
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