  Using anisotropic R-matrices associated with affine Lie algebras $\hat g$
(specifically, $A_{2n}^{(2)}, A_{2n-1}^{(2)}, B_n^{(1)}, C_n^{(1)}, D_n^{(1)}$)
and suitable corresponding K-matrices, we construct families of integrable open
quantum spin chains of finite length, whose transfer matrices are invariant
under the quantum group corresponding to removing one node from the Dynkin
diagram of $\hat g$. We show that these transfer matrices also have a duality
symmetry (for the cases $C_n^{(1)}$ and $D_n^{(1)}$) and additional $Z_2$
symmetries that map complex representations to their conjugates (for the cases
$A_{2n-1}^{(2)}, B_n^{(1)}, D_n^{(1)}$). A key simplification is achieved by
working in a certain "unitary" gauge, in which only the unbroken symmetry
generators appear. The proofs of these symmetries rely on some new properties
of the R-matrices. We use these symmetries to explain the degeneracies of the
transfer matrices.
