The Functors $\mathcal{F}^G_P$ over Local Fields of Positive Characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917716520075264 |
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| author | Linden, Georg |
| author_facet | Linden, Georg |
| contents | Let $G$ be a split connected reductive group over a non-archimedean local field. In the $p$-adic setting, Orlik-Strauch constructed functors from the BGG category $\mathcal{O}$ associated to the Lie algebra of $G$ to the category of locally analytic representation of $G$. We generalize these functors to such groups over non-archimedean local fields of arbitrary characteristic. To this end, we introduce the hyperalgebra of a non-archimedean Lie group $G$, which generalizes its Lie algebra, and consider topological modules over the algebra of locally analytic distributions on $G$ and subalgebras related to this hyperalgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Functors $\mathcal{F}^G_P$ over Local Fields of Positive Characteristic Linden, Georg Representation Theory Number Theory 22E50 (Primary) 20G25, 22E35 (Secondary) Let $G$ be a split connected reductive group over a non-archimedean local field. In the $p$-adic setting, Orlik-Strauch constructed functors from the BGG category $\mathcal{O}$ associated to the Lie algebra of $G$ to the category of locally analytic representation of $G$. We generalize these functors to such groups over non-archimedean local fields of arbitrary characteristic. To this end, we introduce the hyperalgebra of a non-archimedean Lie group $G$, which generalizes its Lie algebra, and consider topological modules over the algebra of locally analytic distributions on $G$ and subalgebras related to this hyperalgebra. |
| title | The Functors $\mathcal{F}^G_P$ over Local Fields of Positive Characteristic |
| topic | Representation Theory Number Theory 22E50 (Primary) 20G25, 22E35 (Secondary) |
| url | https://arxiv.org/abs/2407.06873 |