Colored five-vertex models and Demazure atoms

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Brubaker, Ben¹  Buciumas, Valentin²  Bump, Daniel³  Gustafsson, Henrik P. A.^3,4,5,6,7 

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[4] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[5] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[6] Univ Gothenburg, Dept Math Sci, SE-41296 Gothenburg, Sweden

[7] Chalmers Univ Technol, SE-41296 Gothenburg, Sweden

关键词: Demazure atom;    Lattice model;    Integrability;    The Yang-Baxter equation;    LS keys;   

DOI  :  10.1016/j.jcta.2020.105354

来源: Elsevier

【 摘 要 】

Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a byproduct, we will construct Demazure atoms on Kashiwara's B-infinity crystal and give new algorithms for computing Lascoux-Schutzenberger keys. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free