Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2015) The noncommutative geometry of inner forms of p-adic special linear groups. [MIMS Preprint]
![[thumbnail of innerForms3v8.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
innerForms3v8.pdf Download (553kB) |
Abstract
Let $G$ be any reductive $p$-adic group. We conjecture that every Bernstein component in the space of irreducible smooth $G$-representations can be described as a "twisted extended quotient" of the associated Bernstein torus by the associated finite group. We also pose some conjectures about L-packets and about the structure of the Schwartz algebra of $G$ in these noncommutative geometric terms. Ultimately, our conjectures aim to reduce the classification of irreducible representations to that of supercuspidal representations, and similarly for the local Langlands correspondence. These conjectures generalize earlier versions, which are only expected to hold for quasi-split groups. We prove our conjectures for inner forms of general linear and special linear groups over local non-archimedean fields. This relies on our earlier study of Hecke algebras for types in these groups. We also make the relation with the local Langlands correspondence explicit.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | Inner forms, special linear groups, noncommutative geometry, p-adic |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups |
| Depositing User: | Professor Roger Plymen |
| Date Deposited: | 19 May 2015 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2297 |
Actions (login required)
 |
View Item |