On the universal weight function for the quantum affine algebra
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
DOI:
https://doi.org/10.1090/S1061-0022-2010-01110-5
Published electronically:
May 20, 2010
MathSciNet review:
2584212
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The investigation is continued of the universal weight function for the quantum affine algebra . 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
, 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
, corresponding to two different Gauss decompositions of the fundamental
-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:
https://doi.org/10.1090/S1061-0022-2010-01110-5
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