Lifting banal representations of classical groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908948238434304 |
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| author | Droschl, Johannes |
| author_facet | Droschl, Johannes |
| contents | Let $\mathrm{G}$ be a symplectic or a split orthogonal group over a local non-archimedean field $\mathrm{F}$. A prime $\ell$ is called banal with respect to $\mathrm{G}$ if it does not divide the cardinality of the $k$-points of $\mathrm{G}$, where $k$ is the residue field of $\mathrm{F}$. In this paper we show that for every banal prime $\ell$, any smooth irreducible $\overline{\mathbb{F}}_\ell$-representation of $\mathrm{G}(\mathrm{F})$ admits a lift to $\overline{\mathbb{Q}}_\ell$. We also state similar results for more general classical groups of symplectic, orthogonal or unitary type. As an application we prove Howe-duality in the strongly banal case for symplectic-orthogonal or unitary dual pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lifting banal representations of classical groups Droschl, Johannes Representation Theory Number Theory 11F27, 11S23, 20C20, 22E50 Let $\mathrm{G}$ be a symplectic or a split orthogonal group over a local non-archimedean field $\mathrm{F}$. A prime $\ell$ is called banal with respect to $\mathrm{G}$ if it does not divide the cardinality of the $k$-points of $\mathrm{G}$, where $k$ is the residue field of $\mathrm{F}$. In this paper we show that for every banal prime $\ell$, any smooth irreducible $\overline{\mathbb{F}}_\ell$-representation of $\mathrm{G}(\mathrm{F})$ admits a lift to $\overline{\mathbb{Q}}_\ell$. We also state similar results for more general classical groups of symplectic, orthogonal or unitary type. As an application we prove Howe-duality in the strongly banal case for symplectic-orthogonal or unitary dual pairs. |
| title | Lifting banal representations of classical groups |
| topic | Representation Theory Number Theory 11F27, 11S23, 20C20, 22E50 |
| url | https://arxiv.org/abs/2604.07516 |