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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.11751 |
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Table of 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}.