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Colored five-vertex models and Demazure atoms

Algebra & Discrete Mathematics

Speaker: Dan Bump, Stanford
Related Webpage:
Location: 1147 MSB
Start time: Mon, Oct 21 2019, 12:10PM

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 biproduct, we
construct Demazure atoms on Kashiwara's $\mathcal{B}_\infty$ crystal and
give new algorithms for computing Lascoux-Schützenberger keys.
This is a report on arXiv:1902.01795, and is joint work
with Buciumas, Brubaker and Gustafsson.