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.
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Keywords: Schubert polynomials, Demazure characters, key polynomials, RSK, Edelman–Greene insertion, reduced words.
@article{ALCO_2021__4_2_359_0, author = {Assaf, Sami H.}, title = {A generalization of {Edelman{\textendash}Greene} insertion for {Schubert} polynomials}, journal = {Algebraic Combinatorics}, pages = {359--385}, publisher = {MathOA foundation}, volume = {4}, number = {2}, year = {2021}, doi = {10.5802/alco.160}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.160/} }
TY - JOUR AU - Assaf, Sami H. TI - A generalization of Edelman–Greene insertion for Schubert polynomials JO - Algebraic Combinatorics PY - 2021 SP - 359 EP - 385 VL - 4 IS - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.160/ DO - 10.5802/alco.160 LA - en ID - ALCO_2021__4_2_359_0 ER -
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. http://www.numdam.org/articles/10.5802/alco.160/
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