Newforms in Cuspidal Representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929693500899328 |
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| author | Girsch, Johannes Kurinczuk, Robert |
| author_facet | Girsch, Johannes Kurinczuk, Robert |
| contents | We consider newform vectors in cuspidal representations of $p$-adic general linear groups. We extend the theory from the complex setting to include~$\ell$-modular representations with~$\ell\neq p$, and prove that the conductor is compatible with congruences modulo~$\ell$ for (ramified) supercuspidal~$\ell$-modular representations and for depth zero cuspidals. In the complex and modular setting, we prove explicit formulae for depth zero and minimax cuspidal representations of integral depth, in Bushnell-Kutzko and Whittaker models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newforms in Cuspidal Representations Girsch, Johannes Kurinczuk, Robert Number Theory Representation Theory We consider newform vectors in cuspidal representations of $p$-adic general linear groups. We extend the theory from the complex setting to include~$\ell$-modular representations with~$\ell\neq p$, and prove that the conductor is compatible with congruences modulo~$\ell$ for (ramified) supercuspidal~$\ell$-modular representations and for depth zero cuspidals. In the complex and modular setting, we prove explicit formulae for depth zero and minimax cuspidal representations of integral depth, in Bushnell-Kutzko and Whittaker models. |
| title | Newforms in Cuspidal Representations |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2502.00116 |