Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914115475210240 |
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| author | Ghate, Eknath Le, Daniel Sheth, Mihir |
| author_facet | Ghate, Eknath Le, Daniel Sheth, Mihir |
| contents | Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue field of $F$ extending the earlier results of the authors for $F$ unramified over $\mathbb{Q}_{p}$. This construction uses the theory of diagrams of Breuil and Paskunas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_n(F)$ for $n>2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07281 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$ Ghate, Eknath Le, Daniel Sheth, Mihir Representation Theory Number Theory 22E50, 11S37 Let $p>3$ and $F$ be a non-archimedean local field with residue field a proper finite extension of $\mathbb{F}_p$. We construct smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_2(F)$ defined over the residue field of $F$ extending the earlier results of the authors for $F$ unramified over $\mathbb{Q}_{p}$. This construction uses the theory of diagrams of Breuil and Paskunas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of $\mathrm{GL}_n(F)$ for $n>2$. |
| title | Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$ |
| topic | Representation Theory Number Theory 22E50, 11S37 |
| url | https://arxiv.org/abs/2210.07281 |