Watanabe, Masaki - Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials

dmtcs:2483 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials

Authors: Watanabe, Masaki

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.


Source : oai:HAL:hal-01337821v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Schubert functors,Kraśkiewicz-Pragacz modules,Schubert polynomials,Schubert calculus,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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