  We investigate the canonical quantization in the framework of N=1 simple
supergravity for the case of a very simple gravitational midisuperspace
described by Gowdy $T^3$ cosmological models. We consider supersymmetric
quantum cosmology in the mentioned midisuperspace, where a matrix
representation for the gravitino covector--spinor is used. The full Lorentz
constraint and its implications for the wave function of the universe are
analyzed in detail. We found that there are indeed physical states in the
midisuperspace sector of the theory in contrast to the case of minisuperspace
where there exist no physical states.
