Iwahori-Hecke model for the universal supersingular representation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913997783040000 |
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| author | Chitrao, Anand Soneji, Asfak |
| author_facet | Chitrao, Anand Soneji, Asfak |
| contents | Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$. When $F$ is a finite extension of $\mathbb{Q}_{p}$, Anandavardhanan-Borisagar and Anandavardhanan-Jana introduced an Iwahori-Hecke model for the universal supersingular representation $π_r$ in the regular case $ 0 < r < q-1$. When $F=\mathbb{Q}_{p}$, the first author introduced an Iwahori-Hecke model for $π_r$ when $r = 0, p - 1$. We extend this result to an arbitrary local field $F$ for $r = 0, q - 1$.
We also write down an explicit non-split self-extension of $π_r$ which has a four-dimensional space of $I(1)$-invariants when $F = \mathbb{Q}_p$ and $r = 0, p-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iwahori-Hecke model for the universal supersingular representation Chitrao, Anand Soneji, Asfak Number Theory Representation Theory 20G05, 22E50, 11F70 Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$. When $F$ is a finite extension of $\mathbb{Q}_{p}$, Anandavardhanan-Borisagar and Anandavardhanan-Jana introduced an Iwahori-Hecke model for the universal supersingular representation $π_r$ in the regular case $ 0 < r < q-1$. When $F=\mathbb{Q}_{p}$, the first author introduced an Iwahori-Hecke model for $π_r$ when $r = 0, p - 1$. We extend this result to an arbitrary local field $F$ for $r = 0, q - 1$. We also write down an explicit non-split self-extension of $π_r$ which has a four-dimensional space of $I(1)$-invariants when $F = \mathbb{Q}_p$ and $r = 0, p-1$. |
| title | Iwahori-Hecke model for the universal supersingular representation |
| topic | Number Theory Representation Theory 20G05, 22E50, 11F70 |
| url | https://arxiv.org/abs/2508.13766 |