On the local Langlands correspondence for non-tempered representations
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 unram...
| Verfasser: | |
|---|---|
| Dokumenttypen: | Artikel |
| Erscheinungsdatum: | 2014 |
| Publikation in MIAMI: | 17.10.2014 |
| Datum der letzten Änderung: | 06.11.2015 |
| Quelle: | Münster Journal of Mathematics, 7 (2014) 1, S. 27-50 |
| Angaben zur Ausgabe: | [Electronic ed.] |
| Fachgebiet (DDC): | 510: Mathematik |
| Lizenz: | InC 1.0 |
| Sprache: | English |
| Format: | PDF-Dokument |
| URN: | urn:nbn:de:hbz:6-22359595526 |
| Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-22359595526 |
| Onlinezugriff: | mjm_vol_7_03.pdf |
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 squareintegrable representations of Levi subgroups of G. We establish the basic properties of these new R-groups, which generalize Knapp–Stein R-groups.