On tropical Poisson-Lie theory

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

Global Poisson webinar

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