T–QT–Q relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q  -operator for the quantum XYZ spin chain with open boundary conditions is given by the j→∞j→∞ limit of the corresponding transfer matrix with spin-j   (i.e., (2j+1)(2j+1)-dimensional) auxiliary space. The associated T–QT–Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian.