Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914480024190976 |
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| author | Luo, David C. |
| author_facet | Luo, David C. |
| contents | Let $\text{E}/\text{F}$ be a quadratic extension of non-Archimedean local fields with odd residual characteristic. In this paper, we give equivalent conditions for a simple supercuspidal representation $π$ of $\text{GL}(n, \text{E})$ to be distinguished by $\text{GL}(n, \text{F})$ in terms of its defining maximal simple type and twisted gamma factors. Furthermore, we prove that the collection of twisted gamma factors evaluated at $\frac{1}{2}$ between $π$ and all unitary, tamely ramified quasi-characters of $\text{E}^{\times}$ that are trivial on $\text{F}^{\times}$ is sufficient to determine whether $π$ is distinguished by $\text{GL}(n, \text{F})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$ Luo, David C. Representation Theory Number Theory 22E50, 11F70 Let $\text{E}/\text{F}$ be a quadratic extension of non-Archimedean local fields with odd residual characteristic. In this paper, we give equivalent conditions for a simple supercuspidal representation $π$ of $\text{GL}(n, \text{E})$ to be distinguished by $\text{GL}(n, \text{F})$ in terms of its defining maximal simple type and twisted gamma factors. Furthermore, we prove that the collection of twisted gamma factors evaluated at $\frac{1}{2}$ between $π$ and all unitary, tamely ramified quasi-characters of $\text{E}^{\times}$ that are trivial on $\text{F}^{\times}$ is sufficient to determine whether $π$ is distinguished by $\text{GL}(n, \text{F})$. |
| title | Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$ |
| topic | Representation Theory Number Theory 22E50, 11F70 |
| url | https://arxiv.org/abs/2604.15057 |