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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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


Authors: A. Os'kin, S. Pakuliak and A. Silant'ev
Translated by: the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 4.
Journal: St. Petersburg Math. J. 21 (2010), 651-680
MSC (2010): Primary 81R10
Published electronically: May 20, 2010
MathSciNet review: 2584212
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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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Additional Information

A. Os'kin
Affiliation: Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region 141980, Russia
Email: aoskin@theor.jinr.ru

S. Pakuliak
Affiliation: Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region 141980, and Institute of Theoretical and Experimental Physics, Moscow 117259, Russia
Email: pakuliak@theor.jinr.ru

A. Silant'ev
Affiliation: Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region 141980, Russia, and Départment de Mathématiques, Université d’Angers, 2 Bd. Lavoisier, Angers 49045, France
Email: silant@tonton.univ-angers.fr

DOI: http://dx.doi.org/10.1090/S1061-0022-2010-01110-5
PII: S 1061-0022(2010)01110-5
Keywords: Hierarchical Bethe ansatz, off-shell Bethe vectors, L-operator, current representation
Received by editor(s): July 22, 2008
Published electronically: May 20, 2010
Additional Notes: The work of the second author was supported in part by RFBR, grant no. 05-01-01086, and by the grant NSh-8065.2006.2 for support of leading scientific schools
Article copyright: © Copyright 2010 American Mathematical Society