A remark on decomposing the canonical representation of the Drinfeld curve
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913585855201280 |
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| author | Chen, Zhe Pan, Yushan |
| author_facet | Chen, Zhe Pan, Yushan |
| contents | Recently, by studying an explicit basis, Köck and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof of a weaker version of this result, without specifying a basis. As a by-product we observe a similar decomposition for the Gelfand--Graev representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on decomposing the canonical representation of the Drinfeld curve Chen, Zhe Pan, Yushan Representation Theory Algebraic Geometry Recently, by studying an explicit basis, Köck and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof of a weaker version of this result, without specifying a basis. As a by-product we observe a similar decomposition for the Gelfand--Graev representations. |
| title | A remark on decomposing the canonical representation of the Drinfeld curve |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2411.10194 |