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.
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Accepted:
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DOI: 10.5802/alco.13
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}, pages = {225--247}, publisher = {MathOA foundation}, volume = {1}, number = {2}, year = {2018}, doi = {10.5802/alco.13}, zbl = {06882340}, mrnumber = {3856523}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.13/} }
TY - JOUR AU - Assaf, Sami AU - Schilling, Anne TI - A Demazure crystal construction for Schubert polynomials JO - Algebraic Combinatorics PY - 2018 SP - 225 EP - 247 VL - 1 IS - 2 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.13/ DO - 10.5802/alco.13 LA - en ID - ALCO_2018__1_2_225_0 ER -
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. http://archive.numdam.org/articles/10.5802/alco.13/
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