Hypertoric 2-categories O and symplectic duality

We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category \(\mathcal{O}\). We then establish equivalences of 2-categories...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Gammage, Benjamin, Hilburn, Justin
Format: Article
Language:English
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Sheaves
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Summary:We define 2-categories of microlocal perverse (resp. coherent) sheaves of categories on the skeleton of a hypertoric variety and show that the generators of these 2-categories lift the projectives (resp. simples) in hypertoric category \(\mathcal{O}\). We then establish equivalences of 2-categories categorifying the Koszul duality between Gale dual hypertoric categories \(\mathcal{O}\). These constructions give a prototype for understanding symplectic duality via the fully extended 3d mirror symmetry conjecture.
ISSN:2331-8422