Abstract
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.
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