  We investigate a U(1) lattice chiral gauge theory with domain wall fermions
and gauge fixing. In the reduced model limit, our perturbative and numerical
investigations at Yukawa coupling y=1 show that there are no extra mirror
chiral modes. The longitudinal gauge degrees of freedom have no effect on the
free domain wall fermion spectrum consisting of opposite chiral modes at the
domain wall and the anti-domain wall which have an exponentially damped
overlap. Our numerical investigation at small Yukawa couplings also leads to
similar conclusions as above.
