| Issue |
RAIRO-Theor. Inf. Appl.
Volume 60, 2026
Diophantine Analysis and Related Topics (DART2025Z)
|
|
|---|---|---|
| Article Number | 26 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/ita/2026026 | |
| Published online | 31 July 2026 | |
Restriction of supercuspidal representations
Department of Mathematics and Statistics at Jiangsu Normal University, Xuzhou, Jiangsu 221116, China
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
14
May
2026
Accepted:
27
June
2026
Abstract
We will show that every countably generated unitarizable representation of a group is decomposable. As an application, Suppose (π, V) is a supercuspidal representation of a reductive linear algebraic group G defined over a p-adic field, H is a closed reductive subgroup of G. Then (π|Η, V) can be decomposed into irreducible representations. Moreover, if ZH/(H ⋂ ZG) is compact, then every constituent of (π|Η, V) is supercuspidal; if ZH/(H ⋂ ZG) is non-compact, then every constituent is not admissible.
Mathematics Subject Classification: 22E50 / 20G05
Key words: Unitarizable representations / restricted representations / supercuspidal representations / admissible representations / decomposition / reductive groups
© The authors. Published by EDP Sciences, 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.