  We show that from the spectra of the U_q (sl(2)) symmetric XXZ spin-1/2
finite quantum chain at Delta=-1/2 (q=e^{pi i/3}) one can obtain the spectra of
certain XXZ quantum chains with diagonal and non-diagonal boundary conditions.
Similar observations are made for Delta=0 (q=e^{pi i/2}). In the finite-size
scaling limit the relations among the various spectra are the result of
identities satisfied by known character functions. For the finite chains the
origin of the remarkable spectral identities can be found in the representation
theory of one and two boundaries Temperley-Lieb algebras at exceptional points.
Inspired by these observations we have discovered other spectral identities
between chains with different boundary conditions.
