[Geom., Alg. & Phys.] Crystals and Cluster Algebras
ABSTRACT
Crystal operators on canonical bases as introduced by Kashiwara/Lusztig provide in particular a toolbox to compute within the category of finite dimensional representations of finite dimensional simple Lie algebras. Motivated by this we introduce certain operators on the lattice of tropical points of mirror dual A- and X-cluster spaces. In particular, this yields a crystal-like structure on the canonical basis due to Gross-Hacking-Keel-Kontsevich. (will also be on Zoom: Meeting ID 867 7806 3105, passcode 865611, link https://kias-re-kr.zoom.us/j/86778063105?pwd=0g1p4mcEI0R1SK5IGUTMMI7Vh7gohV.1) (https://sites.google.com/view/gapkias)