The Prism tableau model for Schubert polynomials

Anna Weigandt; Alexander Yong

doi:10.1016/j.jcta.2017.09.009

The Prism tableau model for Schubert polynomials

Anna Weigandt, Alexander Yong

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x₁,x₂,…]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau. Our arguments are developed from the Gröbner geometry of matrix Schubert varieties.

Original language	English (US)
Pages (from-to)	551-582
Number of pages	32
Journal	Journal of Combinatorial Theory. Series A
Volume	154
DOIs	https://doi.org/10.1016/j.jcta.2017.09.009
State	Published - Feb 2018

Keywords

BiGrassmannian permutations
Schubert polynomials
Semistandard tableaux

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2017.09.009

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abstract = "The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,…]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau. Our arguments are developed from the Gr{\"o}bner geometry of matrix Schubert varieties.",

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AB - The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,…]. We suggest the prism tableau model for these polynomials. A novel aspect of this alternative to earlier results is that it directly invokes semistandard tableaux; it does so as part of a colored tableau amalgam. In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau. Our arguments are developed from the Gröbner geometry of matrix Schubert varieties.

KW - BiGrassmannian permutations

KW - Schubert polynomials

KW - Semistandard tableaux

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JF - Journal of Combinatorial Theory. Series A

ER -

The Prism tableau model for Schubert polynomials

Abstract

Keywords

ASJC Scopus subject areas

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