An approach toward Schubert positivities of polynomials using Kra\'skiewicz-Pragacz modules

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.