Related papers: Reflection matrices for the $U_{q}[spo(2n|2m)]$ ve…
The graded reflection equation is investigated for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model. We have found four classes of diagonal solutions and twelve classes of non-diagonal ones. The number of free parameters for some solutions depends…
The graded reflection equation is investigated for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model. We have found four classes of diagonal solutions with at the most one free parameter and twelve classes of non-diagonal ones with the number of…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half…
We propose a classification of the reflection $K$-matrices (solutions of the boundary Yang-Baxter equation) for the $U_{q}[\mathrm{osp}^{\left(2\right)}\left(2|2m\right)]=U_{q}[C^{\left(2\right)}\left(m+1\right)]$ vertex-model. We have…
We consider the insertion of integrable boundaries for a class of supersymmetric quantum models. The generic conditions for constructing purely bosonic, purely fermionic or mixed type solutions of the graded reflection equation are…
We have find the diagonal K matrix solutions of the reflection equations for a class of vertex models. These models have (n+1)(2n+1) vertices and are defined as two set of (n + 1) R matrices, solutions of the equations of Yang-Baxter…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $A_{n-1}^{(1)}$ affine Lie algebra. We have classified them in two classes of solutions. The first class consists…
We investigate the regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $B_{n}^{(1)}$ and $A_{2n}^{(2)}$ affine Lie algebras. In both class of models we find two general solutions with $n+1$ free…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated to the D_{n+1}^(2) affine Lie algebra. We have classified them in terms of three types of K-matrices. The first one have n+2…
We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra…
The symmetries, especially those related to the $R$-transformation, of the reflection equation(RE) for two-component systems are analyzed. The classification of solutions to the RE for eight-, six- and seven-vertex type $R$-matrices is…
In this paper we consider families of multiparametric $R$-matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families of multiparametric $K$-matrices. Our results are indeed…
Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY…
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz…
In this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of reflection matrices for the RSOS model in…
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…
We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution…
We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…
The classification of reflective modular forms is an important problem in the theory of automorphic forms on orthogonal groups. In this paper, we develop an approach based on the theory of Jacobi forms to give a full classification of…
We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric…