Crystals and quasi-crystals: local axioms and connections to quasi-symmetric functions

par Inês Rodrigues (Universidade de Lisboa)

mardi 17 juin 2025, 10:45 → 11:45 Europe/Paris

Salle 112 (ICJ, Université Lyon 1)

Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions. We will introduce a characterization of quasi-crystal graphs by presenting a set of local axioms, and conclude that connected quasi-crystal graphs have a unique highest weight element, whose weight is a composition, and are isomorphic to quasi-crystal graphs of semistandard quasi-ribbon tableaux. We will also explore the interaction of fundamental quasi-symmetric functions and Schur functions, and the arrangement of quasi-crystal components within crystal components.
Based on joint works with Alan Cain, António Malheiro and Fátima Rodrigues.