Exact solution of the trigonometric SU(3) spin chain with generic   off-diagonal boundary reflections
  The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra. 
Guang-Liang Li, Junpeng Cao, Kun Hao, Fakai Wen, Wen-Li Yang and   Kangjie Shi
math-ph cond-mat.stat-mech hep-th math.MP