Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials

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...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 27th...; no. Proceedings; pp. 253 - 260
Main Author: Watanabe, Masaki
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2015
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Computer Science
Discrete Mathematics
kraśkiewicz-pragacz modules
schubert calculus
schubert functors
schubert polynomials
Schubert functors
Kraśkiewicz-Pragacz modules
Schubert polynomials
Schubert calculus
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary: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. Nous employons les modules introduits par Kraśkiewicz et Pragacz (1987, 2004) et démontrons certainespropriétés de positivité des polynômes de Schubert: nous donnons une nouvelle preuve pour le fait classique quele produit de deux polynômes de Schubert est Schubert-positif; nous démontrons aussi un nouveau résultat que lacomposition plethystique d’une fonction de Schur avec un polynôme de Schubert est Schubert-positif. Cet article estun sommaire de ces résultats, et une version pleine de ce travail sera publée ailleurs.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2483