Homological Mirror Symmetry for the universal centralizers I: The adjoint group case

Abstract

We prove homological mirror symmetry for the universal centralizer $J_G$ (a.k.a Toda space), associated to any complex semisimple 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 $G$ has a nontrivial center). This is the first and the main part of a two-part series, dealing with $G$ of adjoint type. The general case will be proved in the forthcoming second part [Jin2].

89 pages, 10 figures. Comments are welcome!

References in corpus (4)

• Gauge theory and mirror symmetry
• Symmetries of categorical representations and the quantum Ngô action
• Sheaf quantization in Weinstein symplectic manifolds
• Non-linear Fourier transforms and the Braverman-Kazhdan conjecture