  We argue that the Hamiltonians for A_{2n}^(2) open quantum spin chains
corresponding to two choices of integrable boundary conditions have the
symmetries U_q(B_n) and U_q(C_n), respectively. We find a formula for the
Dynkin labels of the Bethe states (which determine the degeneracies of the
corresponding eigenvalues) in terms of the numbers of Bethe roots of each type.
With the help of this formula, we verify numerically (for a generic value of
the anisotropy parameter) that the degeneracies and multiplicities of the
spectra implied by the quantum group symmetries are completely described by the
Bethe ansatz.
