Extended quotients in the principal series of reductive p-adic groups

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger (2011) Extended quotients in the principal series of reductive p-adic groups. [MIMS Preprint]

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Abstract

The geometric conjecture developed by the authors in [1,2,3,4] applies to the smooth dual Irr(G) of any reductive p-adic group G. It predicts a definite geometric structure -- the structure of an extended quotient -- for each component in the Bernstein decomposition of Irr(G). In this article, we prove the geometric conjecture for the principal series in any split connected reductive p-adic group G. The proof proceeds via Springer parameters and Langlands parameters. As a consequence of this approach, we establish strong links with the local Langlands correspondence. One important feature of our approach is the emphasis on two-sided cells in extended affine Weyl groups.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Extended quotients, representations of p-adic groups, principal series
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User:	Professor Roger Plymen
Date Deposited:	31 Oct 2011
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1693

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