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2010.106: Geometric structure in the tempered dual of the p-adic group SL(4)

2010.106: Kuok Fai Chao and Roger Plymen (2010) Geometric structure in the tempered dual of the p-adic group SL(4).

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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 2000 > 22 Topological groups, Lie groups
MIMS number:2010.106
Deposited By:Professor Roger Plymen
Deposited On:26 December 2010

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