Demazure crystals for specialized nonsymmetric Macdonald polynomials

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:182

Article

Assaf, Sami¹  Gonzalez, Nicolle² 

[1] Univ Southern Calif, Dept Math, 3620 S Vermont Ave, Los Angeles, CA 90089 USA

[2] Univ Calif Los Angeles, Dept Math, 520 Portola Plaza, Los Angeles, CA 90095 USA

关键词: Demazure crystal;    Demazure character;    Nonsymmetric Macdonald polynomial;    Hall-Littlewood polynomial;    Kostka-Foulkes polynomial;   

DOI  :  10.1016/j.jcta.2021.105463

来源: Elsevier

【 摘 要 】

We give an explicit, nonnegative formula for the expansion of nonsymmetric Macdonald polynomials specialized at t = 0 in terms of Demazure characters. Our formula results from constructing Demazure crystals whose characters are the nonsymmetric Macdonald polynomials, which also gives a new proof that these specialized nonsymmetric Macdonald polynomials are positive graded sums of Demazure characters. Demazure crystals are certain truncations of classical crystals that give a combinatorial skeleton for Demazure modules. To prove our construction, we develop further properties of Demazure crystals, including an efficient algorithm for computing their characters from highest weight elements. As a corollary, we obtain a new formula for the Schur expansion of Hall-Littlewood polynomials in terms of a simple statistic on highest weight elements of our crystals. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free