Euiyong Park : Extended crystal structures of Hernandez-Leclerc categories

lundi 5 déc. 2022, 14:00 → 15:00 Europe/Paris

In this talk, we talk about the categorical crystal structure on the Hernandez-Leclerc category ${\mathcal{C}}_{\mathfrak{g}}^0$. We define extended crystals for quantum groups and show that there is a braid group action on extended crystals.  We then explain how the set of the isomorphism classes of simple modules in ${\mathcal{C}}_{\mathfrak{g}}^0$ has an extended crystal structure, and discuss the braid group action from the viewpoint of the Hernandez-Leclerc category ${\mathcal{C}}_{\mathfrak{g}}^0$. This talk is based on a joint work with M. Kashiwara (arXiv: 2111.07255 and 2207.11644).