An alternative construction of character sheaves on parahoric subgroups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914051984982016 |
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| author | Ivanov, Alexander B. Nie, Sian Yu, Zhihang |
| author_facet | Ivanov, Alexander B. Nie, Sian Yu, Zhihang |
| contents | Inspired by the foundational work of Bezrukavnikov and Chan \cite{BC24} on character sheaves for parahoric subgroups and an alternative interpretation of deep level Deligne-Lusztig characters in \cite{Nie_24}, we present a parallel but closed (non-iterated) construction of character sheaves within the framework of J.--K. Yu's types. We show that our construction yields perverse sheaves, which coincide with those produced in \cite{BC24} in an iterated way. In the regular case we establish the compatibility of their Frobenius traces with deep level Deligne-Lusztig characters. As an application, we prove the positive-depth Springer's hypothesis for arbitrary characters, thereby generalizing the generic case result of Chan and Oi \cite{CO25}. The proofs of our results make critical use of the strategies and results from \cite{BC24} and \cite{Nie_24}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An alternative construction of character sheaves on parahoric subgroups Ivanov, Alexander B. Nie, Sian Yu, Zhihang Representation Theory Algebraic Geometry Inspired by the foundational work of Bezrukavnikov and Chan \cite{BC24} on character sheaves for parahoric subgroups and an alternative interpretation of deep level Deligne-Lusztig characters in \cite{Nie_24}, we present a parallel but closed (non-iterated) construction of character sheaves within the framework of J.--K. Yu's types. We show that our construction yields perverse sheaves, which coincide with those produced in \cite{BC24} in an iterated way. In the regular case we establish the compatibility of their Frobenius traces with deep level Deligne-Lusztig characters. As an application, we prove the positive-depth Springer's hypothesis for arbitrary characters, thereby generalizing the generic case result of Chan and Oi \cite{CO25}. The proofs of our results make critical use of the strategies and results from \cite{BC24} and \cite{Nie_24}. |
| title | An alternative construction of character sheaves on parahoric subgroups |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2509.18442 |