Kazhdan-Laumon Category O, Braverman-Kazhdan Schwartz space, and the semi-infinite flag variety
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915457919877120 |
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| author | Morton-Ferguson, Calder |
| author_facet | Morton-Ferguson, Calder |
| contents | We define and study an analogue of Category O in the context of Kazhdan and Laumon's gluing construction for perverse sheaves on the basic affine space. We explicitly describe the simple objects in this category, and we show its linearized Grothendieck group is isomorphic to a natural submodule of Lusztig's periodic Hecke module. We then provide a categorification of these results by showing that the Kazhdan-Laumon Category O is equivalent to a full subcategory of a suitably-defined category of perverse sheaves on the semi-infinite flag variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03101 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Kazhdan-Laumon Category O, Braverman-Kazhdan Schwartz space, and the semi-infinite flag variety Morton-Ferguson, Calder Representation Theory Algebraic Geometry 14F05 (Primary) 14M15, 20C33, 20G40 (Secondary) We define and study an analogue of Category O in the context of Kazhdan and Laumon's gluing construction for perverse sheaves on the basic affine space. We explicitly describe the simple objects in this category, and we show its linearized Grothendieck group is isomorphic to a natural submodule of Lusztig's periodic Hecke module. We then provide a categorification of these results by showing that the Kazhdan-Laumon Category O is equivalent to a full subcategory of a suitably-defined category of perverse sheaves on the semi-infinite flag variety. |
| title | Kazhdan-Laumon Category O, Braverman-Kazhdan Schwartz space, and the semi-infinite flag variety |
| topic | Representation Theory Algebraic Geometry 14F05 (Primary) 14M15, 20C33, 20G40 (Secondary) |
| url | https://arxiv.org/abs/2210.03101 |