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

  • Anne-Marie Aubert

    Université Pierre et Marie Curie, Paris, France
  • Paul F. Baum

    The Pennsylvania State University, University Park, United States
  • Roger Plymen

    University of Manchester, United Kingdom
  • Maarten Solleveld

    Radboud Universiteit Nijmegen, Netherlands

Abstract

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

Cite this article

Anne-Marie Aubert, Paul F. Baum, Roger Plymen, Maarten Solleveld, Geometric structure for the principal series of a split reductive -adic group with connected centre. J. Noncommut. Geom. 10 (2016), no. 2, pp. 663–680

DOI 10.4171/JNCG/244