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Colored 5-vertex models and Demazure Atoms

Algebra & Discrete Mathematics

Speaker: Daniel Bump, Stanford University
Related Webpage: https://math.stanford.edu/~bump/
Location: 2112 MSB
Start time: Mon, Feb 25 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-SchĂĽtzenberger keys. If time permits, I will also explain how colored six-vertex models can represent Iwahori Whittaker functions. This is joint work with Brubaker, Buciumas and Gustafsson.