  The Lieb-Mattis theorem on the antiferromagnetic ordering of energy levels is
generalized to SU(N) extended Hubbard model with Heisenberg exchange and
pair-hopping terms. It is proved that the minimum energy levels among the
states from equivalent representations are nondegenerate and ordered according
to the dominance order of corresponding Young diagrams. In particular, the
ground states form a unique antisymmetric multiplet. The relation with the
similar ordering among the spatial wavefunctions with different symmetry
classes of ordinary quantum mechanics is discussed also.
