Masaki Watanabe - 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) - https://doi.org/10.46298/dmtcs.2483
Kraśkiewicz-Pragacz modules and some positivity properties of Schubert polynomials

Authors: Masaki Watanabe 1

  • 1 Graduate School of Mathematical Sciences[Tokyo]

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.

https://doi.org/10.46298/dmtcs.2483
Source: 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
Imported on: November 21, 2016
Keywords: Schubert functors,Kraśkiewicz-Pragacz modules,Schubert polynomials,Schubert calculus,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)

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Source : ScholeXplorer IsRelatedTo ARXIV alg-geom/9703001
Source : ScholeXplorer IsRelatedTo DOI 10.1215/s0012-7094-98-09511-4
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.alg-geom/9703001
  • 10.48550/arxiv.alg-geom/9703001
  • alg-geom/9703001
  • 10.1215/s0012-7094-98-09511-4
  • 10.1215/s0012-7094-98-09511-4
Schubert polynomials, the Bruhat order, and the geometry of flag manifolds

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