We clarify the extra signs appearing in the graded quantum Yang–Baxter reflection equations, when they are written in a matrix form. We find the boundary K-matrix for the Perk–Schultz six-vertex model, thus give a general solution to the graded reflection equation associated with it.
In this work, we employ the algebraic-differential method recently developed by the author to solve the Yang-Baxter equation for arbitrary fifteen-vertex models satisfying the ice-rule. We show that there are four different families of such regular R matrices containing several free-parameters. The corresponding reflection K matrices, solutions of the boundary Yang-Baxter equation, were also found and classified. We found that there are three different families of regular K matrices, regardless of what R matrix we choose.