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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2412.11751 |
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| _version_ | 1866929633157447680 |
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| author | Das, Arpan |
| author_facet | Das, Arpan |
| contents | Let $p$ be a prime and $F$ a non-archimedean local field of residue characteristic $p$. In this paper, we study the restriction of smooth irreducible $\bar{\mathbb{F}}_p$-representations of $\mathrm{SL}_2(F)$ to its Borel subgroup. In essence, we show that the action of $\mathrm{SL}_2(F)$ on its irreducibles is controlled by the action of the Borel subgroup. The results of this paper constitute the $\mathrm{SL}_2$-analogue of a work of Paškūnas\cite{PaskunasRestriction}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11751 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A restriction problem for mod-$p$ representations of $\mathrm{SL}_2(F)$ Das, Arpan Representation Theory Let $p$ be a prime and $F$ a non-archimedean local field of residue characteristic $p$. In this paper, we study the restriction of smooth irreducible $\bar{\mathbb{F}}_p$-representations of $\mathrm{SL}_2(F)$ to its Borel subgroup. In essence, we show that the action of $\mathrm{SL}_2(F)$ on its irreducibles is controlled by the action of the Borel subgroup. The results of this paper constitute the $\mathrm{SL}_2$-analogue of a work of Paškūnas\cite{PaskunasRestriction}. |
| title | A restriction problem for mod-$p$ representations of $\mathrm{SL}_2(F)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.11751 |