Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2013) On the local Langlands correspondence for non-tempered representations. [MIMS Preprint]
![[thumbnail of LLCnontempered11.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
LLCnontempered11.pdf Download (459kB) |
Abstract
Let $G$ be a reductive $p$-adic group. We study how a local Langlands correspondence for irreducible tempered $G$-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of $G$. We prove that, under a natural condition involving compatibility with unramified twists, this is possible in a canonical way. To this end we introduce analytic R-groups associated to non-tempered essentially square-integrable representations of Levi subgroups of $G$. We establish the basic properties of these new R-groups, which generalize Knapp-Stein R-groups.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | reductive $p$-adic group, representation theory, R-group, local Langlands conjecture |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups |
| Depositing User: | Professor Roger Plymen |
| Date Deposited: | 23 Jul 2013 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1999 |
Actions (login required)
 |
View Item |