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TMF, 2019, Volume 201, Number 2, Pages 153–174 (Mi tmf9762)  

Bethe vectors for orthogonal integrable models

A. N. Liashyka, S. Z. Pakuliakb, E. Ragoucyc, N. A. Slavnovb

a Skolkovo Institute of Science and Technology, Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
c Laboratoire de Physique Théorique LAPTh, CNRS and USMB, Annecy-le-Vieux, France

Abstract: We consider quantum integrable models associated with the $\mathfrak{so}_3$ algebra and describe Bethe vectors of these models in terms of the current generators of the $\mathcal{D}Y(\mathfrak{so}_3)$ algebra. To implement this program, we use an isomorphism between the $R$-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type $B$-, $C$-, and $D$-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the $\mathfrak{so}_3$ algebra.

Keywords: Yangian of a simple Lie algebra, Yangian double, algebraic Bethe ansatz.

Funding Agency Grant Number
Russian Science Foundation 19-11-00062
This research was performed at the Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, and is supported by a grant from the Russian Science Foundation (Project No. 19-11-00062).


DOI: https://doi.org/10.4213/tmf9762

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English version:
Theoretical and Mathematical Physics, 2019, 201:2, 1545–1564

Received: 07.06.2019
Revised: 07.06.2019

Citation: A. N. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Bethe vectors for orthogonal integrable models”, TMF, 201:2 (2019), 153–174; Theoret. and Math. Phys., 201:2 (2019), 1545–1564

Citation in format AMSBIB
\Bibitem{LiaPakRag19}
\by A.~N.~Liashyk, S.~Z.~Pakuliak, E.~Ragoucy, N.~A.~Slavnov
\paper Bethe vectors for orthogonal integrable models
\jour TMF
\yr 2019
\vol 201
\issue 2
\pages 153--174
\mathnet{http://mi.mathnet.ru/tmf9762}
\crossref{https://doi.org/10.4213/tmf9762}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 2
\pages 1545--1564


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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