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SUMMARY:Euiyong Park : Extended crystal structures of Hernandez-Leclerc ca
 tegories
DTSTART:20221205T130000Z
DTEND:20221205T140000Z
DTSTAMP:20260421T034100Z
UID:indico-event-9031@indico.math.cnrs.fr
DESCRIPTION:In this talk\, we talk about the categorical crystal structure
  on the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. We defi
 ne extended crystals for quantum groups and show that there is a braid gro
 up action on extended crystals.  We then explain how the set of the isomo
 rphism classes of simple modules in $\\mathscr{C}_\\mathfrak{g}^0$ has an 
 extended crystal structure\, and discuss the braid group action from the v
 iewpoint of the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$.
  This talk is based on a joint work with M. Kashiwara (arXiv: 2111.07255 a
 nd 2207.11644).\n\nhttps://indico.math.cnrs.fr/event/9031/
URL:https://indico.math.cnrs.fr/event/9031/
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