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Hypertoric 2-categories O and symplectic duality

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arxiv 2310.06172 v2 pith:7C2G2NWA submitted 2023-10-09 math.RT hep-thmath.AGmath.SG

Benjamin Gammage , Justin Hilburn This is my paper · ORCID
classification math.RThep-thmath.AGmath.SG
keywords categorieshypertoricdualitymathcalrespsymplecticcategorifyingcategory
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abstract

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.

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  1. Nonabelian shift operators and shifted Yangians

    math.AG 2024-12 conditional novelty 6.0 of 10

    New nonabelian shift operators and wall-crossing identities show that the quantized Coulomb branch of pure GL_n gauge theory is a quotient of the shifted Yangian Y_{-nα}(sl2), with vertex functions as Hecke eigenfunctions.

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