An approach towards Schubert positivities of polynomials using Kraśkiewicz–Pragacz modules

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