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.
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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).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 2, pp. 153–174, November, 2019.
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Liashyk, A.N., Pakuliak, S.Z., Ragoucy, E. et al. Bethe Vectors for Orthogonal Integrable Models. Theor Math Phys 201, 1545–1564 (2019). https://doi.org/10.1134/S0040577919110023
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DOI: https://doi.org/10.1134/S0040577919110023