Combinatorics of canonical bases and cluster duality

Thursday, March 15, 2018 - 13:00
Speaker Information
Bea Schumann

Abstract or Additional Information

In this talk we explain how the string parametrization of the canonical basis of a representation of a simple, simply connected, simply laced algebraic group over the complex numbers arises from the tropicalizations of a potential function on a cluster variety in the setup of Gross-Hacking-Keel-Kontsevich. We further discuss the relation between this potential function and Berenstein-Kazhdan's decoration function appearing in the setup of geometric crystals. This is joint work with Volker Genz and Gleb Koshevoy.