Quaternionic symplectic model for discrete series representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917224260829184 |
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| author | Matringe, Nadir Suzuki, Miyu |
| author_facet | Matringe, Nadir Suzuki, Miyu |
| contents | Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is $\mathrm{Sp}_n(D)$-distinguished only if it is supercuspidal. Here, $\mathrm{Sp}_n(D)$ is the quaternionic symplectic group. Combined with the recent study on $\mathrm{Sp}_n(D)$-distinguished supercuspidal representations by Sécherre and Stevens, this completes the classification of $\mathrm{Sp}_n(D)$-distinguished discrete series representations, as predicted by Dipendra Prasad. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic symplectic model for discrete series representations Matringe, Nadir Suzuki, Miyu Representation Theory Number Theory 22E50, 11F70 Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is $\mathrm{Sp}_n(D)$-distinguished only if it is supercuspidal. Here, $\mathrm{Sp}_n(D)$ is the quaternionic symplectic group. Combined with the recent study on $\mathrm{Sp}_n(D)$-distinguished supercuspidal representations by Sécherre and Stevens, this completes the classification of $\mathrm{Sp}_n(D)$-distinguished discrete series representations, as predicted by Dipendra Prasad. |
| title | Quaternionic symplectic model for discrete series representations |
| topic | Representation Theory Number Theory 22E50, 11F70 |
| url | https://arxiv.org/abs/2507.16364 |