Discrete series representations of quaternionic ${\rm GL}_n(D)$ with symplectic periods
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908789190426624 |
|---|---|
| author | Matringe, Nadir Sécherre, Vincent Stevens, Shaun Suzuki, Miyu |
| author_facet | Matringe, Nadir Sécherre, Vincent Stevens, Shaun Suzuki, Miyu |
| contents | For a non-Archimedean locally compact field $F$ of odd residue characteristic and characteristic $0$, we prove a conjecture of D. Prasad predicting that, for an integer $n \geq 1$ and a non-split quaternionic $F$-algebra $D$, a discrete series representation of ${\rm GL}_n(D)$ has a symplectic period if and only if it is cuspidal and its Jacquet--Langlands transfer to ${\rm GL}_{2n}(F)$ is non-cuspidal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete series representations of quaternionic ${\rm GL}_n(D)$ with symplectic periods Matringe, Nadir Sécherre, Vincent Stevens, Shaun Suzuki, Miyu Representation Theory Number Theory 22E50, 11F70 For a non-Archimedean locally compact field $F$ of odd residue characteristic and characteristic $0$, we prove a conjecture of D. Prasad predicting that, for an integer $n \geq 1$ and a non-split quaternionic $F$-algebra $D$, a discrete series representation of ${\rm GL}_n(D)$ has a symplectic period if and only if it is cuspidal and its Jacquet--Langlands transfer to ${\rm GL}_{2n}(F)$ is non-cuspidal. |
| title | Discrete series representations of quaternionic ${\rm GL}_n(D)$ with symplectic periods |
| topic | Representation Theory Number Theory 22E50, 11F70 |
| url | https://arxiv.org/abs/2503.08955 |