On the universal weight function for the quantum affine algebra 𝑈_{𝑞}(̂𝔤𝔩_{𝔑})

Os′kin, A.; Pakuliak, S.; Silant′ev, A.

doi:10.1090/S1061-0022-2010-01110-5

On the universal weight function for the quantum affine algebra $U_q(\widehat {\mathfrak {gl}}_N)$
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by A. Os′kin, S. Pakuliak and A. Silant′ev
Translated by: the authors

St. Petersburg Math. J. 21 (2010), 651-680

DOI: https://doi.org/10.1090/S1061-0022-2010-01110-5

Published electronically: May 20, 2010

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Abstract:

The investigation is continued of the universal weight function for the quantum affine algebra $U_q(\widehat {\mathfrak {gl}}_N)$. Two recurrence relations are obtained for the universal weight function with the help of the method of projections. On the level of the evaluation representation of $U_q(\widehat {\mathfrak {gl}}_N)$, two recurrence relations are reproduced, which were calculated earlier for the off-shell Bethe vectors by combinatorial methods. One of the results of the paper is a description of two different but isomorphic currents or “new” realizations of the algebra $U_q(\widehat {\mathfrak {gl}}_N)$, corresponding to two different Gauss decompositions of the fundamental $\mathrm {L}$-operators.

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