An approach toward Schubert positivities of polynomials using Kraśkiewicz-Pragacz modules
arXiv:1406.6203
Abstract
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 a filtration by Kraśkiewicz-Pragacz modules. In finding criteria for 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.
added explanations; corrected a mistake in the proof of Proposition 6.4