  In this paper, we investigate properties of modules introduced by
Kra\'skiewicz and Pragacz which realize Schubert polynomials as their
characters. In particular, we give some characterizations of modules having a
filtration by Kra\'skiewicz-Pragacz modules. In finding criteria for
filtrations, we calculate generating sets for the annihilator ideals of the
lowest vectors in Kra\'skiewicz-Pragacz modules, and derive a projectivity
result concerning Kra\'skiewicz-Pragacz modules.
