Spectral equivalences and symmetry breaking in integrable SU_q(N) spin   chains with boundaries
  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. 
A. Nichols