We find new families of solutions of the $D_{ n+1}^{ (2)}$ boundary Yang-Baxter equation. The open spin-chain transfer matrices constructed with these K-matrices have quantum group symmetry corresponding to removing one node from the $D_{ n+1}^{ (2)}$ Dynkin diagram, namely, $U_{ q}(B_{ n-p}) \otimes U_{ q}(B_{ p})$, where $p=0, \ldots, n$. These transfer matrices also have a $p \leftrightarrow n-p$ duality symmetry. These symmetries help to account for the degeneracies in the spectrum of the transfer matrix.
Categories: hep-th cond-mat.stat-mech math-ph math.MP math.QA