Geodesic
Bethe vectors for orthogonal integrable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 153-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. N. Liashyk; S. Z. Pakuliak; E. Ragoucy; N. A. Slavnov. Bethe vectors for orthogonal integrable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 153-174. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a1/

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