Séminaire d'algèbre

Euiyong Park : Extended crystal structures of Hernandez-Leclerc categories

Europe/Paris
Description

In this talk, we talk about the categorical crystal structure on the Hernandez-Leclerc category Cg0. 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 Cg0 has an extended crystal structure, and discuss the braid group action from the viewpoint of the Hernandez-Leclerc category Cg0. This talk is based on a joint work with M. Kashiwara (arXiv: 2111.07255 and 2207.11644).