Related papers: The general crossing relation for boundary reflect…
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 present paper is devoted to the study of backward stochastic differential equations with mean reflection formulated by Briand et al. [7]. We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on…
We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic…
We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary…
Yang-Baxter bialgebras, as previously introduced by the authors, are shown to arise from a double crossproduct construction applied to the bialgebra R T T = T T R, E T = T E R, \Delta(T) = T \hat{\otimes} T, \Delta(E) = E \hat{\otimes} T +…
Given a right-non-degenerate set-theoretic solution $(X,r)$ to the Yang-Baxter equation, we construct a whole family of YBE solutions $r^{(k)}$ on $X$ indexed by its reflections $k$ (i.e., solutions to the reflection equation for $r$). This…
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 construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS…
We explore the reflection-transmission quantum Yang-Baxter equations, arising in factorized scattering theory of integrable models with impurities. The physical origin of these equations is clarified and three general families of solutions…
One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to…
Integral formulae for the correlation functions of the XYZ model with a boundary are calculated by mapping the model to the bosonized boundary SOS model. The boundary K-matrix considered here coincides with the known general solution of the…
We study the integrable and supersymmetric massive $\hat\phi_{(1,3)}$ deformation of the tricritical Ising model in the presence of a boundary. We use constraints from supersymmetry in order to compute the exact boundary $S$-matrices, which…
We use boundary quantum group symmetry to obtain recursion formulas which determine nondiagonal solutions of the boundary Yang-Baxter equation (reflection equation) of the XXZ type for any spin j.
An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to…
We construct $2^n$-families of solutions of the Yang-Baxter equation from $n$-products of three-dimensional $R$ and $L$ operators satisfying the tetrahedron equation. They are identified with the quantum $R$ matrices for the Hopf algebras…
We propose explicit expressions for the boundary reflection matrices of the ${\cal A}_m+(r,s)$ series of massive scattering theories, obtained by perturbing the ${\cal A}_m$ unitary minimal models with $(r,s)$ boundary conditions with both…
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and only the 2-dimensional representation of…
We survey the matrix product solutions of the Yang-Baxter equation obtained recently from the tetrahedron equation. They form a family of quantum $R$ matrices of generalized quantum groups interpolating the symmetric tensor representations…
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…