Smooth duals of inner forms of gln and sln

Anne Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld

Research output: Contribution to journalArticlepeer-review


Let F be a non-archimedean local field. We prove that every Bernstein component in the smooth dual of each inner form of the general linear group GLn(F) is canonically in bijection with the extended quotient for the action, given by Bernstein, of a finite group on a complex torus. For inner forms of SLn(F) we prove that each Bernstein component is canonically in bijection with the associated twisted extended quotient. In both cases, the bijections satisfy naturality properties with respect to the tempered dual, parabolic induction, central character, and the local Langlands correspondence.

Original languageEnglish (US)
Pages (from-to)373-420
Number of pages48
JournalDocumenta Mathematica
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics


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