ALGEBRAIC COMBINATORICS

no. 2
A Demazure crystal construction for Schubert polynomials
Assaf, Sami1; Schilling, Anne2
1 Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, U.S.A.
2 Department of Mathematics, UC Davis, One Shields Ave., Davis, CA 95616-8633, U.S.A.
Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 225-247.

Stanley symmetric functions are the stable limits of Schubert polynomials. In this paper, we show that, conversely, Schubert polynomials are Demazure truncations of Stanley symmetric functions. This parallels the relationship between Schur functions and Demazure characters for the general linear group. We establish this connection by imposing a Demazure crystal structure on key tableaux, recently introduced by the first author in connection with Demazure characters and Schubert polynomials, and linking this to the type A crystal structure on reduced word factorizations, recently introduced by Morse and the second author in connection with Stanley symmetric functions.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.13
Classification: 14N15, 05E10, 05A05, 05E05, 05E18, 20G42
Keywords: Schubert polynomials, Demazure characters, Stanley symmetric functions, crystal bases
Assaf, Sami 1; Schilling, Anne 2

1 Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, U.S.A.
2 Department of Mathematics, UC Davis, One Shields Ave., Davis, CA 95616-8633, U.S.A.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Assaf, Sami; Schilling, Anne. A Demazure crystal construction for Schubert polynomials. Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 225-247. doi : 10.5802/alco.13. https://alco.centre-mersenne.org/articles/10.5802/alco.13/

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