On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916426275618816 |
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| author | Nadimpalli, Santosh Sheth, Mihir |
| author_facet | Nadimpalli, Santosh Sheth, Mihir |
| contents | Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the integrality of generic irreducible locally algebraic representations. In this article, we prove the sufficiency of Emerton's conditions for some tamely ramified locally algebraic representations of $\mathrm{GL}_{2}(D)$ where $D$ is a $p$-adic division algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08218 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$ Nadimpalli, Santosh Sheth, Mihir Representation Theory Number Theory 11F70, 22E50 Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the integrality of generic irreducible locally algebraic representations. In this article, we prove the sufficiency of Emerton's conditions for some tamely ramified locally algebraic representations of $\mathrm{GL}_{2}(D)$ where $D$ is a $p$-adic division algebra. |
| title | On the integrality of locally algebraic representations of $\mathrm{GL}_{2}(D)$ |
| topic | Representation Theory Number Theory 11F70, 22E50 |
| url | https://arxiv.org/abs/2304.08218 |