Exact solution of the $A^{(1)}_{n-1}$ trigonometric vertex model with   non-diagonal open boundaries
  The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained. 
Wen-Li Yang and Yao-Zhong Zhang