On tropical Poisson-Lie theory

Yanpeng Li (Sichuan University)

25-Nov-2021, 13:15-14:15 (14 months ago)

Abstract: For a compact Lie group $K$ with the standard Poisson structure, we first construct a tropical version for the dual Poisson-Lie group $K^\ast$. This construction will then help us 1) to establish a relation between $K^\ast$ and the Langlands dual group $G^\vee$ of the complexification $G:=K^\mathbb{C}$; 2) to construct an exhaustion by symplectic embeddings of toric domains for each regular coadjoint orbit of $K$. We combine ideas from Poisson-Lie groups, cluster algebras and the geometric crystals of Berenstein-Kazhdan.

The talk is based on joint works with A. Alekseev, A. Berenstein, B. Hoffman, and J. Lane.

mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic