The integrable general open-boundary conditions for the one-dimensional Bariev chain are considered. All kinds of solutions to the reflection equation (RE) and its dual are obtained.
The integrable open-boundary conditions for the one-dimensional Bariev chain are considered. The diagonal boundary K matrices are found and the commuting transfer matrix is constructed. Since the local monodromy matrix as well as the quantum R matrix do not possess the crossing symmetry, our construction shows that Sklyanin's formalism may be extended to apply to any one-dimensional systems integrable by the quantum inverse scattering method.