On the local Langlands correspondence for non-tempered representations

Titelaufnahme

Titel
On the local Langlands correspondence for non-tempered representations
Verfasser
Aubert, Anne-Marie ; Baum, Paul Frank ; Plymen, Roger ; Solleveld, Maarten
Enthalten in
Münster Journal of Mathematics, H. Münster Journal of Mathematics, S. 27-50
Erschienen
2014
Sprache
Englisch
Dokumenttyp
Aufsatz in einer Zeitschrift
URN
urn:nbn:de:hbz:6-22359595526

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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 squareintegrable 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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