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 |
Available Versions of this Item
- Geometric structure in the tempered dual of the p-adic group SL(4) (deposited 20 April 2011)
- Geometric structure in the tempered dual of the p-adic group SL(4) (deposited 26 December 2010) [Currently Displayed]
- Geometric structure in the tempered dual of the p-adic group SL(4) (deposited 16 December 2010)
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