On a t-exactness property of the Harish-Chandra transform
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913604287070208 |
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| author | Gonin, Roman Ionov, Andrei Tolmachov, Kostiantyn |
| author_facet | Gonin, Roman Ionov, Andrei Tolmachov, Kostiantyn |
| contents | Using hyperbolic localization, we identify the nearby cycles along the Vinberg degeneration with the composition of Radon and Harish-Chandra functors, both considered for the category of character sheaves. This provides a new, simple proof of the exactness of this composition, extending previously known results to arbitrary monodromy and more general sheaf-theoretic set-ups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a t-exactness property of the Harish-Chandra transform Gonin, Roman Ionov, Andrei Tolmachov, Kostiantyn Representation Theory Algebraic Geometry Using hyperbolic localization, we identify the nearby cycles along the Vinberg degeneration with the composition of Radon and Harish-Chandra functors, both considered for the category of character sheaves. This provides a new, simple proof of the exactness of this composition, extending previously known results to arbitrary monodromy and more general sheaf-theoretic set-ups. |
| title | On a t-exactness property of the Harish-Chandra transform |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2412.07146 |