Colored five-vertex models and Demazure atoms
Journal article, 2021
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∞ crystal and give new algorithms for computing Lascoux-Schützenberger keys.
LS keys
Integrability
Lattice model
Demazure atom
The Yang-Baxter equation
Author
Ben Brubaker
University of Minnesota
Valentin Buciumas
University of Queensland
Daniel Bump
Stanford University
Henrik Gustafsson
Stanford University
Rutgers University
Institute for Advanced Studies
Chalmers, Mathematical Sciences, Algebra and geometry
Journal of Combinatorial Theory - Series A
0097-3165 (ISSN) 10960899 (eISSN)
Vol. 178 105354Subject Categories
Probability Theory and Statistics
Discrete Mathematics
Mathematical Analysis
DOI
10.1016/j.jcta.2020.105354