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J. Phys. A, 2014, Volume 47, Issue 10, 105202, 16 pages (Mi jpha14)  

Bethe vectors of quantum integrable models based on $U_q(\hat{\mathfrak{gl}}_N)$

S. Pakuliakabc, E. Ragoucyd, N. A. Slavnove

a Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Moscow reg., Russia
b Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia
c Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
d Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie, BP 110, F-74941 Annecy-le-Vieux Cedex, France
e Steklov Mathematical Institute, Moscow, Russia

Abstract: We study quantum $U_q(\widehat{\mathfrak {gl}}_{N})$ integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by certain morphisms of the positive Borel subalgebra in $U_q(\widehat{\mathfrak {gl}}_{N})$ into analogous subalgebra in $U_{q^{-1}}(\widehat{\mathfrak {gl}}_N)$.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00980-a
11-01-00440-a
13-01-12405-ofi-m
National Research University Higher School of Economics 12-09-0064
Agence Nationale de la Recherche Blanc ANR SIMI1 2010-BLAN-0120-02
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation SS-4612.2012
The work of SP was supported in part by RFBR grant 11-01-00980-a and grant of Scientific Foundation of NRU HSE 12-09-0064. ER was supported by ANR Project DIADEMS (Programme Blanc ANR SIMI1 2010-BLAN-0120-02). NAS was supported by the Program of RAS Basic Problems of the Nonlinear Dynamics, RFBR-11-01-00440-a, RFBR-13-01-12405-ofi-m2, SS-4612.2012.


DOI: https://doi.org/10.1088/1751-8113/47/10/105202


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Received: 12.11.2013
Accepted:20.12.2013
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