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A.-M. Aubert, P. Baum, R. Plymen, and M. Solleveld: “On the local Langlands correspondence for non-tempered representations,” Münster J. Math. 7 : 1 (2014), pp. 27–50. Dedicated to Peter Schneider on the occasion of his 60th birthday. MR 3271238 Zbl 06382808 ArXiv 1303.0828 article

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 \( \mathrm{R} \)-groups associated to non-tempered essentially square-integrable representations of Levi subgroups of \( G \). We establish the basic properties of these new \( \mathrm{R} \)-groups, which generalize Knapp–Stein \( \mathrm{R} \)-groups.

Anne-Marie Aubert	Related
Roger J. Plymen	Related
Peter Schneider	Related
Maarten Solleveld	Related