On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model

Abstract: In this paper we consider families of multiparametric $R$-matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families of multiparametric $K$-matrices. Our results are indeed non-trivial generalization of the $K$-matrix solutions of the {\cal {U}}{q}[D{n+1}^{(2)}] vertex model when distinct reflections and extra free-parameters are admissible.