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arXiv · 2107.13395

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

Xin Jin
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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].

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Xin Jin. 2021-07-28. Homological Mirror Symmetry for the universal centralizers I: The adjoint group case. https://arxiv.org/abs/2107.13395

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