A Demazure crystal construction for Schubert polynomials
Algebraic Combinatorics, Volume 1 (2018) no. 2, p. 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 : 2017-08-11
Revised : 2017-11-21
Accepted : 2017-12-27
DOI : https://doi.org/10.5802/alco.13
Classification:  14N15,  05E10,  05A05,  05E05,  05E18,  20G42
Keywords: Schubert polynomials, Demazure characters, Stanley symmetric functions, crystal bases
@article{ALCO_2018__1_2_225_0,
     author = {Assaf, Sami and Schilling, Anne},
     title = {A Demazure crystal construction for Schubert polynomials},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {1},
     number = {2},
     year = {2018},
     pages = {225-247},
     doi = {10.5802/alco.13},
     language = {en},
     url = {http://alco.centre-mersenne.org/item/ALCO_2018__1_2_225_0}
}
Assaf, Sami;Schilling, Anne. A Demazure crystal construction for Schubert polynomials. Algebraic Combinatorics, Volume 1 (2018) no. 2, p. 225-247. doi : 10.5802/alco.13. https://alco.centre-mersenne.org/item/ALCO_2018__1_2_225_0/

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