Demazure Atoms and the Yang-Baxter Equation
Schur polynomials are the characters of irreducible representations of GL(n). Demazure Atoms are pieces of Schur polynomials, or corresponding sets of tableaux. They were defined by Lascoux and Schützenberger in the 1970's. Many algorithms have been given to decide which atom contains a given tableaux by computing its "Lascoux-Schützenberger key".
On the other hand solvable lattice models are a topic in statistical mechanics, in which certain systems can be studied using a special tool, the Yang-Baxter equation. We will exhibit systems whose partition functions are Demazure atoms and obtain a new, very simple algorithm for computing Lascoux-Schützenberger keys. The proofs are a mixture of Yang-Baxter equation and combinatorial methods.
This is a report on arXiv:1902.01795. It is joint work with Brubaker, Buciumas and Gustafsson.