  We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal
integrable boundary terms.
  The algebraic study of spin chains with different types of boundary terms is
used to motivate a set of spectral equivalences between integrable chains with
purely diagonal boundary terms and ones with an arbitrary non-diagonal term at
one end. For each choice of diagonal boundary terms there is an isospectral
one-boundary problem and vice-versa.
  The quantum group SU_q (N) symmetry is broken by the presence of a
non-diagonal boundary term however one can use the spectral equivalence with
the diagonal chain to easily understand the residual symmetries of the system.
