Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras
Mirković–Vilonen polytopes and Khovanov–Lauda–Rouquier algebras
We describe how Mirkovic-Vilonen polytopes arise naturally from the categorification of Lie algebras using Khovanov-Lauda-Rouquier algebras. This gives an explicit description of the unique crystal isomorphism between simple representations of the KLR algebra and MV polytopes. MV polytopes, as defined from the geometry of the affine Grassmannian, only make sense …