A note on the non-diagonal K-matrices for the trigonometric   $A^{(1)}_{n-1}$ vertex model
  This note presents explicit matrix expressions of a class of recently-discovered non-diagonal K-matrices for the trigonometric $A^{(1)}_{n-1}$ vertex model. From these explicit expressions, it is easily seen that in addition to a {\it discrete} (positive integer) parameter $l$, $1\leq l\leq n$, the K-matrices contain $n+1$ (or $n$) continuous free boundary parameters. 
Wen-Li Yang and Yao-Zhong Zhang