Related papers: Baxterization of solutions to reflection equation …
An algebraic approach to integrable quantum field theory with a boundary (a half line) is presented and interesting algebraic equations, Reflection equations (RE) and Reflection Bootstrap equations (RBE) are discussed. The Reflection…
Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on…
We define a concept of Hecke algebra for structure groups of set-theoretical solutions to the Yang--Baxter equation. As a comparison to Artin--Tits groups of spherical type, we study some properties of this construction, while also…
We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of…
The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix…
The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix…
We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke…
We provide a dual version of the Geck--Rouquier Theorem on the center of an Iwahori--Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank $2$, for which the symmetrising trace conjecture is…
The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…
New development of the theory of Grothendieck polynomials, based on an exponential solution of the Yang-Baxter equation in the algebra of projectors are given.
Given a skew left brace $B$, a method is given to construct all the non-degenerate set-theoretic solutions $(X,r)$ of the Yang Baxter equation such that the associated permutation group $\mathcal{G}(X,r)$ is isomorphic, as a skew left…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the graded version of the $A_{n-1}^{(1)}$ affine Lie algebra, the $U_{q}[sl(m|n)^{(1)}]$ vertex model, also known as…
In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The associated…
We study the $G_2$ reflection equation for the three particles in $1+1$ dimension that undergo a special scattering/reflections described by the Pappus theorem. It is a sixth order equation and serves as a natural $G_2$ analogue of the…
We study the rational solution of the Yang-Baxter equation with the supersymmetry algebra sl(2|1). The R-matrix acting in the tensor product of two arbitrary representations of the supersymmetry algebra can be represented as the product of…
We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or $A_{1}^{(1)}$ model, Izergin-Korepin or $A_{2}^{(2)}$ model, sl(2|1) model and osp(2|1) model. We find…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.
We present a generalization of the theory of quantum symmetric pairs as developed by Kolb and Letzter. We introduce a class of generalized Satake diagrams that give rise to (not necessarily involutive) automorphisms of the second kind of…
We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…
We present particularly simple new solutions to the Yang--Baxter equation arising from two--dimensional cyclic representations of quantum $SU(2)$. They are readily interpreted as scattering matrices of relativistic objects, and the quantum…