  Employing the spin-flavor representation, we investigate the structures of
the doubler-mixing symmetries and the mechanisms of their spontaneous breakdown
in four types of lattice fermion formulation. We first revisit the
$U(4)\timesU(4)A$ symmetries of the naive fermion with the vanishing bare mass
m, and re-express them in terms of the spin-flavor representation. We apply the
same method to the Wilson fermion, which possesses only the U(1) vector
symmetry for general values of m. For a special value of m, however, there
emerges an additional U(1) symmetry to be broken by pion condensation. We also
explore two types of minimally doubled fermion, and discover a similar kind of
symmetry enhancement and its spontaneous breakdown.
