A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915862437429248 |
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| author | Dong, Junbin |
| author_facet | Dong, Junbin |
| contents | Let $\bf T$ be the group of diagonal matrices in $SL_2(\bar{\mathbb{F}}_p)$, where $p$ is a prime number. Let $\Bbbk$ be an algebraically closed field of characteristic not equal to $2$ and $p$. We classify all the irreducible $\Bbbk$-representations of $SL_2(\bar{\mathbb{F}}_p)$ that admit $\bf T$-stable lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13769 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic Dong, Junbin Representation Theory Let $\bf T$ be the group of diagonal matrices in $SL_2(\bar{\mathbb{F}}_p)$, where $p$ is a prime number. Let $\Bbbk$ be an algebraically closed field of characteristic not equal to $2$ and $p$. We classify all the irreducible $\Bbbk$-representations of $SL_2(\bar{\mathbb{F}}_p)$ that admit $\bf T$-stable lines. |
| title | A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2603.13769 |