The principal series of $p$-adic groups with disconnected centre

Abstract

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 centre of G. This leads to a local Langlands correspondence for principal series representations, which satisfies all expected properties. We also prove that the ABPS conjecture about the geometric structure of Bernstein components is valid throughout the principal series of G.

This is a revised and abridged version of part 3 of "Geometric structure and the local Langlands correspondence" (arXiv:1211.0180). In v2 some proofs involving temperedness and square-integrability were worked out in more detail (pages 30-31 and 51-53)

References in corpus (1)

• Conjectures about p-adic groups and their noncommutative geometry

Cited by in corpus (6)

• Affine Hecke algebras for Langlands parameters
• A uniform classification of discrete series representations of affine Hecke algebras
• Affine Hecke algebras for classical p-adic groups
• Conjectures about p-adic groups and their noncommutative geometry
• Proof of the Aubert-Baum-Plymen-Solleveld conjecture for split classical groups
• A nonabelian Fourier transform for tempered unipotent representations