Abstract
We consider the SUq(N) invariant spin chain with diagonal and non-diagonal integrable boundary terms.
The algebraic study of spin chains with different kinds 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 iso-spectral one-boundary problem and vice versa. The cases N = 2, 3, 4 are used as examples throughout to illustrate the general structure.
The quantum group SUq(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. This is described in detail for the case of SU(3).