  The smallness and hierarchy in fermion parameters could be the result of
selection rules due to an Abelian horizontal symmetry broken by a small
parameter. When applied to the lepton sector, then for a large class of models,
a number of interesting order of magnitude relations arise: with $i<j$,
$m(\nu_i)/m(\nu_j)\sim\sin^2\theta_{ij}$;
$m(\ell^-_i)/m(\ell^-_j)\lsim\sin\theta_{ij}$; $m(\nu_i)/m(\nu_j)\gsim
m^2(\ell^-_i)/m^2(\ell^-_j)$; $m(\nu_e)\lsim m(\nu_\mu)\lsim m(\nu_\tau)$. The
relations between neutrino masses and mixings may become exact if the
horizontal symmetry together with holomorphy induce certain zero entries in the
lepton mass matrices. A full high energy theory is likely to include scalars
with flavor changing couplings and heavy leptons in vector representations;
however, the masses of these particles are too heavy to be directly observed in
experiment. Indirect evidence for the horizontal symmetry may arise from other
sectors of the theory: non-degenerate sleptons are allowed as the symmetry
aligns lepton and slepton mass matrices; light leptoquarks are allowed as the
symmetry can make their couplings diagonal and chiral.
