30 November 2021 to 2 December 2021
Le Bois-Marie
Europe/Paris timezone

Crystal Operators on Cluster Algebras (Remote)

30 Nov 2021, 14:50
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Volker Genz (IBS CGP)


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. We expect these operators to have a wider range of applications in the theory of cluster algebras and in physics. This is partially based on joint work with Gleb Koshevoy and Bea Schumann.

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