On the local Langlands correspondence for non-tempered representations

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.

minor corrections in version 2

References in corpus (3)

• Dual R-groups of the inner forms of SL(N)
• Geometric structure and the local Langlands conjecture
• Transfer of R-groups between p-adic inner forms of SL_n

Cited by in corpus (3)

• Hecke algebras for inner forms of p-adic special linear groups
• Conjectures about p-adic groups and their noncommutative geometry
• Local Langlands Correspondence for Unitary Groups via Theta Lifts