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:	16 Dec 2010
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1554

Available Versions of this Item

• Geometric structure in the tempered dual of the p-adic group SL(4). (deposited 16 Dec 2010) [Currently Displayed]
  • Geometric structure in the tempered dual of the p-adic group SL(4). (deposited 26 Dec 2010)
    • Geometric structure in the tempered dual of the p-adic group SL(4). (deposited 20 Apr 2011)

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