Homological Mirror Symmetry for the universal centralizers

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).

arXiv comment119 pages, 11 figures. This is a merge and revision of arXiv:2107.13395 and the previous version of this post, following the referee's suggestions