  The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is
considered. For the first type, the Hamiltonian is hermitian but not for the
second type which includes the U_{q}[SU(2)] symmetric case. It is shown that
for a certain `tuning' between the anisotropy angle and the boundary terms the
spectra present unexpected degeneracies. These degeneracies are related to the
structure of the irreducible representations of the Virasoro algebras for c<1.
