Related papers: On the Symmetries of Integrability
We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group…
Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group $\mathrm{SL}(2,\mathbb{C})$ or Faddeev's modular…
We study the Yang-Baxter equation for the $R$-matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized…
From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first…
Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlev\'e property as the number of equations in each `integrable system' increases. Certain…
We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral…
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…
To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter…
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…
This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group ${\cal U}_{q}[X_{n}]$ for the affine Lie algebras $X_{n}$ = $A_{1}^{(1)}$,…
The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article…
We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a…
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…
A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a…
Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the set…