Lifting polynomial representations of $\mathrm{SL}_2(p^r)$ from $\mathbb{F}_p$ to $\mathbb{Z}/p^s\mathbb{Z}$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918212811096064 |
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| author | Parker, Chris van Beek, Martin |
| author_facet | Parker, Chris van Beek, Martin |
| contents | We describe all of the irreducible polynomial $\mathbb{F}_p\mathrm{SL}_2(p^r)$ representations which lift to $(\mathbb{Z}/p^s\mathbb{Z})\mathrm{SL}_2(p^r)$ representations for $s>1$, observing that they almost never do. We also show that two related indecomposable $\mathbb{F}_p \mathrm{SL}_2(p^r)$ representations cannot be lifted to $\mathbb{Z}/p^s\mathbb{Z}$ representations for $s>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lifting polynomial representations of $\mathrm{SL}_2(p^r)$ from $\mathbb{F}_p$ to $\mathbb{Z}/p^s\mathbb{Z}$ Parker, Chris van Beek, Martin Representation Theory Group Theory 20C33, 20C11 We describe all of the irreducible polynomial $\mathbb{F}_p\mathrm{SL}_2(p^r)$ representations which lift to $(\mathbb{Z}/p^s\mathbb{Z})\mathrm{SL}_2(p^r)$ representations for $s>1$, observing that they almost never do. We also show that two related indecomposable $\mathbb{F}_p \mathrm{SL}_2(p^r)$ representations cannot be lifted to $\mathbb{Z}/p^s\mathbb{Z}$ representations for $s>1$. |
| title | Lifting polynomial representations of $\mathrm{SL}_2(p^r)$ from $\mathbb{F}_p$ to $\mathbb{Z}/p^s\mathbb{Z}$ |
| topic | Representation Theory Group Theory 20C33, 20C11 |
| url | https://arxiv.org/abs/2411.16379 |