We give a crystal-theoretic proof that nonsymmetric Macdonald polynomials specialized to are affine Demazure characters. We explicitly construct an affine Demazure crystal on semistandard key tabloids such that removing the affine edges recovers the finite Demazure crystals constructed earlier by the authors. We also realize the filtration on highest weight modules by Demazure modules by defining explicit embedding operators which, at the level of characters, parallels the recursion operators of Knop and Sahi for specialized nonsymmetric Macdonald polynomials. Thus we prove combinatorially in type A that every affine Demazure module admits a finite Demazure flag.
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Keywords: Affine Demazure crystal, affine Demazure character, nonsymmetric Macdonald polynomial
@article{ALCO_2021__4_5_777_0, author = {Assaf, Sami and Gonz\'alez, Nicolle}, title = {Affine {Demazure} crystals for specialized nonsymmetric {Macdonald} polynomials}, journal = {Algebraic Combinatorics}, pages = {777--793}, publisher = {MathOA foundation}, volume = {4}, number = {5}, year = {2021}, doi = {10.5802/alco.178}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.178/} }
TY - JOUR AU - Assaf, Sami AU - González, Nicolle TI - Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials JO - Algebraic Combinatorics PY - 2021 SP - 777 EP - 793 VL - 4 IS - 5 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.178/ DO - 10.5802/alco.178 LA - en ID - ALCO_2021__4_5_777_0 ER -
%0 Journal Article %A Assaf, Sami %A González, Nicolle %T Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials %J Algebraic Combinatorics %D 2021 %P 777-793 %V 4 %N 5 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.178/ %R 10.5802/alco.178 %G en %F ALCO_2021__4_5_777_0
Assaf, Sami; González, Nicolle. Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials. Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 777-793. doi : 10.5802/alco.178. http://www.numdam.org/articles/10.5802/alco.178/
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