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2011.88: Extended quotients in the principal series of reductive p-adic groups

2011.88: Anne-Marie Aubert, Paul Baum and Roger Plymen (2011) Extended quotients in the principal series of reductive p-adic groups.

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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 2000 > 20 Group theory and generalizations
MSC 2000 > 22 Topological groups, Lie groups
MIMS number:2011.88
Deposited By:Professor Roger Plymen
Deposited On:31 October 2011

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