Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization

Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1

Let $G$ be a connected semisimple Lie group. There are two natural duality constructions that assign to it the Langlands dual group $G^{\vee }$ and the Poisson-Lie dual group $G^{\ast }$. T…