ALGEBRAIC COMBINATORICS

no. 2
A generalization of Edelman–Greene insertion for Schubert polynomials
Assaf, Sami H.1
1 Department of Mathematics University of Southern California 3620 South Vermont Avenue Los Angeles, CA 90089-2532, U.S.A.
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 359-385.

Edelman and Greene generalized the Robinson–Schensted–Knuth correspondence to reduced words in order to give a bijective proof of the Schur positivity of Stanley symmetric functions. Stanley symmetric functions may be regarded as the stable limits of Schubert polynomials, and similarly Schur functions may be regarded as the stable limits of Demazure characters for the general linear group. We modify the Edelman–Greene correspondence to give an analogous, explicit formula for the Demazure character expansion of Schubert polynomials. Our techniques utilize dual equivalence and its polynomial variation, but here we demonstrate how to extract explicit formulas from that machinery which may be applied to other positivity problems as well.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.160
Classification: 05A05, 05A15, 05A19, 14N15
Keywords: Schubert polynomials, Demazure characters, key polynomials, RSK, Edelman–Greene insertion, reduced words.
Assaf, Sami H. 1

1 Department of Mathematics University of Southern California 3620 South Vermont Avenue Los Angeles, CA 90089-2532, U.S.A.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Assaf, Sami H. A generalization of Edelman–Greene insertion for Schubert polynomials. Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 359-385. doi : 10.5802/alco.160. https://alco.centre-mersenne.org/articles/10.5802/alco.160/

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