Bethe vectors for orthogonal integrable models

Abstract

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

arXiv comment22 pages

References in corpus (13)

• On the R-matrix realization of Yangians and their representations
• Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
• Combinatorial Formulae for Nested Bethe Vectors
• Highest coefficient of scalar products in SU(3)-invariant integrable models
• Bethe eigenvectors of higher transfer matrices
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• Weight function for the quantum affine algebra $U_q({\widehat{sl}}_3)$
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Weight function for the quantum affine algebra $U_q(A_2^{(2)})$
• Weight functions and Drinfeld currents

Cited by in corpus (7)

• Liouville reflection operator, affine Yangian and Bethe ansatz
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• Spinorial R operator and Algebraic Bethe Ansatz
• On the R-matrix realization of quantum loop algebras
• Isomorphism between twisted $q$-Yangians and affine $ı$quantum groups: type AI
• Algebraic Bethe ansatz for ${\mathfrak{o}}_{2n+1}$-invariant integrable models
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models