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).
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.09035
- arXiv:
- arXiv:2206.09035
- Bibcode:
- 2022arXiv220609035J
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Symplectic Geometry
- E-Print:
- 119 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