Homological Mirror Symmetry for the universal centralizers

TL;DR

This paper proves homological mirror symmetry for the universal centralizer associated with any complex reductive Lie group, relating symplectic and algebraic categories in a new setting.

Contribution

It establishes the homological mirror symmetry equivalence for the universal centralizer, expanding the class of known mirror pairs to include Toda spaces.

Findings

Homological mirror symmetry holds for the universal centralizer $J_G$.

The A-side is a partially wrapped Fukaya category on $J_G$.

The B-side is the category of coherent sheaves on a quotient of a dual maximal torus.

Abstract

We prove homological mirror symmetry for the universal centralizer $J_G$ (a.k.a the Toda space), associated to any complex reductive Lie group $G$. The A-side is a partially wrapped Fukaya category on $J_G$, and the B-side is the category of coherent sheaves on the categorical quotient of a dual maximal torus by the Weyl group action (with some modification if the center of $G$ is not connected).