On the universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)

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We continue investigation of the universal weight function for the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_N)$ started in arXiv:math/0610517 and arXiv:0711.2819.

• We obtain two recurrence relations for the universal weight function applying the method of projections developed in arXiv:math/0610398.
• On the level of the evaluation representation of $U_q(\hat{\mathfrak{gl}}_N)$ we reproduce both recurrence relations for the off-shell Bethe vectors calculated in arXiv:math/0702277 using combinatorial methods.