Hypertoric 2-categories O and symplectic duality
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909558601940992 |
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| author | Gammage, Benjamin Hilburn, Justin |
| author_facet | Gammage, Benjamin Hilburn, Justin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06172 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypertoric 2-categories O and symplectic duality Gammage, Benjamin Hilburn, Justin Representation Theory High Energy Physics - Theory Algebraic Geometry Symplectic Geometry 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. |
| title | Hypertoric 2-categories O and symplectic duality |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2310.06172 |