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arXiv · 1303.0828

On the local Langlands correspondence for non-tempered representations

Anne-Marie Aubert·Paul Baum·Roger Plymen·Maarten Solleveld
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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.

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Anne-Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld. 2014-02-28. On the local Langlands correspondence for non-tempered representations. https://arxiv.org/abs/1303.0828

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