Geodesic
Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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We use the modules introduced by Kraśkiewicz and Pragacz (1987, 2004) to show some positivity propertiesof Schubert polynomials. We give a new proof to the classical fact that the product of two Schubert polynomialsis Schubert-positive, and also show a new result that the plethystic composition of a Schur function with a Schubertpolynomial is Schubert-positive. The present submission is an extended abstract on these results and the full versionof this work will be published elsewhere. 
@article{DMTCS_2015_special_285_a27,
     author = {Watanabe, Masaki},
     title = {Kra\'skiewicz-Pragacz modules and some positivity properties of {Schubert} polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2483},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2483/}
}
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Watanabe, Masaki. Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2483. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2483/

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