The principal series of p -adic groups with disconnected center

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

Research output: Contribution to journalArticlepeer-review


Let G be a split connected reductive group over a local non-Archimedean field. We classify all irreducible complex G-representations in the principal series, irrespective of the (dis)connectedness of the center of G. This leads to a local Langlands correspondence for principal series representations of G. It satisfies all expected properties, in particular it is functorial with respect to homomorphisms of reductive groups. At the same time, we show that every Bernstein component s in the principal series has the structure of an extended quotient of Bernstein's torus by Bernstein's finite group (both attached to s).

Original languageEnglish
Pages (from-to)798-854
Number of pages57
JournalProceedings of the London Mathematical Society
Issue number5
Publication statusPublished - 2017


  • 20G05
  • 22E50 (primary)


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