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

Anne-Marie Aubert; Paul Baum; Roger Plymen; Maarten Solleveld

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

Representation Theory 2017-08-09 v2

Authors: Anne-Marie Aubert , Paul Baum , Roger Plymen , Maarten Solleveld

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.

Keywords

p-adic groups principal series irreducible representations local Langlands correspondence Bernstein components ABPS conjecture reductive groups

Cite

@article{arxiv.1409.8110,
  title  = {The principal series of $p$-adic groups with disconnected centre},
  author = {Anne-Marie Aubert and Paul Baum and Roger Plymen and Maarten Solleveld},
  journal= {arXiv preprint arXiv:1409.8110},
  year   = {2017}
}

Comments

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)

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

Abstract

Keywords

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