A Demazure crystal construction for Schubert polynomials

Abstract

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.

18 pages, 16 figures; version 2: references added and updated

References in corpus (3)

• Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams
• Set-Valued Skyline Fillings
• Combinatorial models for Schubert polynomials

Cited by in corpus (8)

• Demazure crystals for Kohnert polynomials
• Crystal structures for symmetric Grothendieck polynomials
• Colored five-vertex models and Demazure atoms
• Grothendieck to Lascoux expansions
• Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials
• Locks fit into keys: a crystal analysis of lock polynomials
• Hybrid Pipe Dreams for Key Polynomials
• The "Young" and "reverse" dichotomy of polynomials