Geometric structure for the principal series of a split reductive -adic group with connected centre
Anne-Marie Aubert
Université Pierre et Marie Curie, Paris, FrancePaul F. Baum
The Pennsylvania State University, University Park, United StatesRoger Plymen
University of Manchester, United KingdomMaarten Solleveld
Radboud Universiteit Nijmegen, Netherlands
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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