  We propose a scheme combining spin reflection positivity and generalized
hole-particle and orbital transformations to characterize the symmetry
properties of the ground state for some correlated electron models on bipartite
lattices. In particular, we rigorously determine at half-filling and for
different regions of the parameter space the spin, orbital and $\eta$ pairing
pseudospin of the ground state of generalized two-orbital Hubbard models which
include the Hund's rule coupling.
