Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

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

Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

Representation Theory 2016-12-09 v2

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

Abstract

Let $\mathcal{G}$ be a split reductive $p$ -adic group with connected centre. We show that each Bernstein block in the principal series of $\mathcal{G}$ admits a definite geometric structure, namely that of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form $T//W$ where $T$ is a maximal torus in the Langlands dual group of $\mathcal{G}$ and $W$ is the Weyl group of $\mathcal{G}$ .

Keywords

p-adic group principal series Bernstein block extended quotient Iwahori-spherical block Langlands dual

Cite

@article{arxiv.1408.0673,
  title  = {Geometric structure for the principal series of a split reductive $p$-adic group with connected centre},
  author = {Anne-Marie Aubert and Paul Baum and Roger Plymen and Maarten Solleveld},
  journal= {arXiv preprint arXiv:1408.0673},
  year   = {2016}
}

Comments

16 pages. This version is more concise, and there is a corresponding change of title. It supersedes the relevant part of arXiv:1211.0180

Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

Abstract

Keywords

Cite

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