  We study the influence of the quadratic Zeeman effect in the Mott-insulator
phases of hard-core spin-3/2 fermions. We show that contrary to spinor bosons,
any quadratic Zeeman coupling preserves a $SU(2)\otimes SU(2)$ symmetry,
leading for large-enough quadratic Zeeman coupling to an isotropic
pseudo-spin-1/2 Heisenberg antiferromagnet. Depending on the scattering
lengths, on 1D lattices the quadratic Zeeman coupling can induce either a
Kosterlitz-Thouless transition between a gapped dimerized spin-3/2 phase and a
gapless pseudo-spin-1/2 antiferromagnet, or a commensurate-incommensurate
transition from a gapless spin-liquid into the pseudo-spin-1/2 antiferromagnet.
Similar arguments allow to foresee corresponding transitions on ladder type and
square lattices. We analyze various observables which should reveal in
experiments these phases.
