Discrete series representations of quaternionic GL 𝑛 (𝐷) with symplectic periods
Abstract For a non-Archimedean locally compact field 𝐹 of odd residue characteristic and characteristic 0, we prove a conjecture of Prasad predicting that, for an integer n ⩾ 1 n\geqslant 1 and a non-split quaternionic 𝐹-algebra 𝐷, a discrete series representation of GL n ( D ) \operatorname{GL}_{n}(D) has a symplectic period if and only if it is cuspidal and its Jacquet–Langlands transfer to GL 2 n ( F ) \operatorname{GL}_{2n}(F) is non-cuspidal.
Authors
- Miyu Suzuki (ORCID: https://orcid.org/0000-0001-7770-3837)
- Nadir Matringe (ORCID: https://orcid.org/0000-0003-3064-2525)
- Vincent Sécherre
- Shaun Stevens (ORCID: https://orcid.org/0000-0003-1399-7332)
Institutions
- University of East Anglia (GB)
- Centre National de la Recherche Scientifique (FR)
- Université de Versailles Saint-Quentin-en-Yvelines (FR)
- Kyoto University (JP)
- Université Paris-Saclay (FR)
- Laboratoire de Mathématiques Blaise Pascal (FR)
Publication Details
- Journal
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Published
- 2026-10-16
- DOI
- https://doi.org/10.1515/crelle-2026-0084
- Primary Topic
- Advanced Algebra and Geometry
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Engineering and Physical Sciences Research Council
- Japan Society for the Promotion of Science