  SU(4) dynamical symmetry is shown to imply a no-double-occupancy constraint
on the minimal symmetry description of antiferromagnetism and d-wave
superconductivity. This implies a maximum doping fraction of 1/4 for cuprates
and provides a microscopic critique of the projected SO(5) model. We propose
that SU(4) superconductors are representative of a class of compounds that we
term non-abelian superconductors. We further suggest that non-abelian
superconductors may exist having SU(4) symmetry and therefore cuprate-like
dynamics, but without d-wave hybridization.
