Spectrum of the supersymmetric t-J model with non-diagonal open boundaries

In this work we diagonalize the double-row transfer matrix of the supersymmetric t-J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes of solutions are found, one diagonal solution and other non-diagonal. Except for the case of two non-diagonal boundaries, the eigenvalues are given for arbitrary values of the boundary parameters.