Geometric structure in the tempered dual of the p-adic group SL(4)

Chao, Kuok Fai and Plymen, Roger (2010) Geometric structure in the tempered dual of the p-adic group SL(4). [MIMS Preprint]

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Abstract

We confirm the Aubert-Baum-Plymen conjecture for part of the tempered dual of the p-adic group SL(4). This requires some very detailed representation theory. Of special interest is the case of SL(4,Q_2). Here, there is a tetrahedron of reducibility, and the extended quotient performs a deconstruction: it creates the ordinary quotient and six unit intervals. The six intervals are then assembled into the six edges of a tetrahedron, and create a perfect model of reducibility. The L-packets in this article all conform to the L-packet conjecture in http://eprints.ma.man.ac.uk/1504.

Item Type: MIMS Preprint
Uncontrolled Keywords: Special linear group, p-adic group, representations, extended quotient
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 26 Dec 2010
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1555

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