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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.08393 |
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| _version_ | 1866910222832893952 |
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| author | Matringe, Nadir |
| author_facet | Matringe, Nadir |
| contents | Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations of Kato and Takano. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On relative cuspidality Matringe, Nadir Representation Theory Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations of Kato and Takano. |
| title | On relative cuspidality |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2506.08393 |