2014/09/30 by Anne-Marie Aubert, Paul Baum, Roger Plymen +1
Mathematics · #math.RT #msc:20C08 #msc:20G05 #msc:22E50
published as Proc. London Math. Soc. 114.5 (2017), 798-854 · 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)
arxiv created 2015/11/03 · arxiv updated 2017/08/09
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.