# Bethe Vectors for Orthogonal Integrable Models

@article{Liashyk2019BetheVF, title={Bethe Vectors for Orthogonal Integrable Models}, author={A Liashyk and S Z Pakuliak and Eric Ragoucy and Nikita Andreevich Slavnov}, journal={Theoretical and Mathematical Physics}, year={2019} }

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…

## 9 Citations

Algebraic Bethe ansatz for
$$\mathfrak o_{2n+1}$$
-invariant integrable models

- MathematicsTheoretical and Mathematical Physics
- 2021

Abstract We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the $$ \mathfrak{o}…

Actions of the monodromy matrix elements onto $\mathfrak{g}\mathfrak{l}\left(m\vert n\right)$-invariant Bethe vectors

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

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…

Liouville reflection operator, affine Yangian and Bethe ansatz

- Mathematics
- 2020

In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik-Okounkov $R$-matrix. We discuss the relation between $RLL$ and current…

Integrable crosscap states in $\mathfrak{gl}(N)$ spin chains

- Mathematics
- 2022

: We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the gl ( N ) symmetric models. We also give a derivation for the exact overlaps between the…

Spinor Representations of Orthogonal and Symplectic Yangians

- Mathematics
- 2020

Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with $so(n)$ or $sp(2m)$ symmetry. We study representations…

Why scalar products in the algebraic Bethe ansatz have determinant representation

- MathematicsJournal of High Energy Physics
- 2019

Abstract
We show that the scalar products of on-shell and off-shell Bethe vectors in the algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this…

On the R-matrix realization of quantum loop algebras

- ArtSciPost Physics
- 2022

<jats:p>We consider <jats:inline-formula><jats:alternatives><jats:tex-math>r</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"…

Actions of the monodromy matrix elements onto gl(m|n)-invariant Bethe vectors

- Mathematics
- 2020

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

## References

SHOWING 1-10 OF 46 REFERENCES

New symmetries of gl(N)-invariant Bethe vectors

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing -invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original…

Current presentation for the super-Yangian double and Bethe vectors

- Physics, Mathematics
- 2017

Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto…

Bethe eigenvectors of higher transfer matrices

- Mathematics
- 2006

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there…

Weight Function for the Quantum Affine Algebra Uq(
$$\widehat{\mathfrak{s}\mathfrak{l}}_3$$
)

- Mathematics
- 2005

AbstractWe give a precise expression for the universal weight function of the quantum affine algebra Uq(
$$\widehat{\mathfrak{s}\mathfrak{l}}_3$$
). The calculations use the technique of projecting…

On the R-Matrix Realization of Yangians and their Representations

- Mathematics
- 2006

Abstract.We study the Yangians $${\text{Y}}(\mathfrak{a})$$ associated with the simple Lie algebras $$\mathfrak{a}$$ of type B, C or D. The algebra $${\text{Y}}(\mathfrak{a})$$ can be regarded as a…

Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D

- MathematicsCommunications in Mathematical Physics
- 2018

It is well-known that the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between…

Highest coefficient of scalar products in SU(3)-invariant integrable models

- Mathematics
- 2012

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their…