Weight function and nested Bethe ansatz
type: Item
instance of: scholarly article
title: Weight function and nested Bethe ansatz
zbMATH Open document ID: 1116.17010
published in: Annales Henri Poincaré
publication date: 2007-02-14T00:00:00Z
review text: The paper is devoted to the comparison of two constructions of weight functions for the quantum algebra \(U_q(\widehat{\mathfrak{gl}}_N)\), the first being given in terms of \(L\)-operators and the second being defined in terms of projections according to the approach formulated in [\textit{S. Khoroshkin} and \textit{S. Pakuliak}, ``Weight function for the quantum affine algebra \(U_q(\widehat{\mathfrak{sl}}_3)\)'', Theor. Math. Phys. 145, No. 1, 1373--1399 (2005); \textit{B. Enriquez, S. Khoroshkin} and \textit{S. Pakuliak}, ``Weight functions and Drinfeld current''s, Preprint-ITEP-TH-40/05 (math/0610398)]. To this aim, projections of the product of the Drinfeld's currents onto intersections of the different Borel subalgebras in the current realization of the quantum affine algebra \(U_q(\widehat{\mathfrak{gl}}_N)\) are calculated. The author proves coincidence of the two construction for the symmetric tensor products of the fundamental vector representation of \(U_q(\widehat{ \mathfrak{g l}}_N)\) by resorting to the isomorphism between \(L\)-operator and current formulation of \(U_q(\widehat{ \mathfrak{g l}}_N)\) established in [\textit{J. Ding} and \textit{I. B. Frenkel}, ``Isomorphism of two realizations of quantum affine algebra \(U_q(\widehat{\mathfrak{gl}}_N)\)'', Commun. Math. Phys. 156, No. 2, 277--300 (1993; Zbl 0786.17008)] and by demonstrating that identical recursion relations on the rank \(N\) are satisfied. A slightly extended discussion of the problem can be found in [\textit{S. Khoroshkin, S. Pakuliak} and \textit{V. Tarasov}, ``Off-shell Bethe vectors and Drinfeld currents'', J. Geom. Phys. 57, No. 8, 1713--1732 (2007; Zbl 1148.17010)].
reviewed by: G. Landolfi
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R12
zbMATH DE Number: 5126617
zbMATH Keywords: quantum integrable models
zbMATH Keywords: quantum affine algebras
author: Stanislav Z. Pakuliak
MaRDI profile type: Publication
full work available at URL: s00023-006-0291-7
OpenAlex ID: W2026364290
DOI: 10.1007/S00023-006-0291-7
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description: scientific article; zbMATH DE number 5126617