An approach toward Schubert positivities of polynomials using Kra\'skiewicz-Pragacz modules
Representation Theory
2015-07-06 v4 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1406.6203,
title = {An approach toward Schubert positivities of polynomials using Kra\'skiewicz-Pragacz modules},
author = {Masaki Watanabe},
journal= {arXiv preprint arXiv:1406.6203},
year = {2015}
}
Comments
added explanations; corrected a mistake in the proof of Proposition 6.4