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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
2014-08-22.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. |
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