Combinatorial Formulae for Nested Bethe Vectors

We give combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for tensor products of irreducible evaluation modules over the Yangian $Y({\mathfrak{gl}}_N)$ and the quantum affine algebra $U_q(\widetilde{\mathfrak{gl}_N})$. The results of the paper were obtained in 1998 and were used in math.QA/9905137, math.QA/0302148, math.QA/0610517.

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