Orateur
Prof.
Volker Genz
(IBS CGP)
Description
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 previously introduced certain operators on the lattice of tropical points of mirror dual A- and X-cluster spaces. In this talk, we give an update. In particular, the crystal structure gives rise to a binary operation on the canonical basis due to Gross-Hacking-Keel-Kontsevich. We expect this to have a wider range of applications in the theory of cluster algebras and physics.
