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Related papers: Bethe Vectors in Quantum Integrable Models with Cl…

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We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}_3$-invariant $R$-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We…

Mathematical Physics · Physics 2018-07-04 A. Liashyk , N. A. Slavnov

We consider $\mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also…

Mathematical Physics · Physics 2019-09-09 S. Belliard , N. A. Slavnov

We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients.…

Mathematical Physics · Physics 2025-07-23 A. Liashyk , S. Pakuliak , E. Ragoucy

A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type $\mathfrak{gl}_n$ or type $\mathfrak{o}_{2n+1}$ symmetries. These recurrence relations describe how…

Quantum Algebra · Mathematics 2025-09-23 Andrii Liashyk , Stanislav Pakuliak , Eric Ragoucy

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…

Mathematical Physics · Physics 2019-11-19 A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q(\mathfrak{gl}_N)$-invariant $R$-matrices. The action formulas allow to…

Mathematical Physics · Physics 2022-05-06 A. Liashyk , S. Z. Pakuliak

We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker…

Mathematical Physics · Physics 2016-12-21 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is investigated in the framework of algebraic Bethe ansatz method. A construction of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the Drinfeld…

Mathematical Physics · Physics 2021-12-13 A. Liashyk , S. Z. Pakuliak

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…

Mathematical Physics · Physics 2015-08-03 Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov

We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe…

Mathematical Physics · Physics 2016-11-24 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant $R$-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix.…

Mathematical Physics · Physics 2019-05-22 A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the $\mathfrak{gl}(m|n)$-invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the…

Mathematical Physics · Physics 2021-12-13 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…

Mathematical Physics · Physics 2013-10-08 Samuel Belliard , Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov

We study quantum Uq(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…

Mathematical Physics · Physics 2015-06-17 S. Pakuliak , E. Ragoucy , N. A. Slavnov

Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors…

Mathematical Physics · Physics 2017-03-14 Jan Fuksa

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These…

Mathematical Physics · Physics 2015-06-11 S. Belliard , S. Pakuliak , E. Ragoucy , N. A. Slavnov

The note deals with the Gaudin model associated with the tensor product of n irreducible finite-dimensional sl_{N+1}-modules marked by distinct complex numbers z_1,..., z_n. The Bethe Ansatz is a method to construct common eigenvectors of…

Representation Theory · Mathematics 2007-05-23 S. Chmutov , I. Scherbak

We study $\mathfrak{gl}(2|1)$ symmetric integrable models solvable by the nested algebraic Bethe ansatz. Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors. We show that…

Mathematical Physics · Physics 2016-10-11 Arthur Hutsalyuk , Andrii Liashyk , Stanislav Z. Pakuliak , Eric Ragoucy , Nikita A. Slavnov

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum…

Mathematical Physics · Physics 2018-03-01 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q(\widehat{gl}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the product of the transfer matrix and…

Quantum Algebra · Mathematics 2015-05-13 L. Frappat , S. Khoroshkin , S. Pakuliak , E. Ragoucy
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