Chao, Kuok Fai (2010) Geometric structure in the tempered dual of SL(N). Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.
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Abstract
The Aubert-Baum-Plymen conjecture says that there is a simple geometric structure within the representation theory of p-adic groups such as SL(N). This PhD thesis will focus on SL(2), SL(3) and SL(4). We prove the conjecture for SL(2); part (3) of the conjecture for SL(3); and the principal series case for SL(4, Q_p) with p >2. The constructions are, for the most part, very explicit. One case is especially interesting: we reveal a tetrahedron of reducibility in the tempered dual of SL(4, Q_2).
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | Representation theory, special linear group |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups |
| Depositing User: | Professor Roger Plymen |
| Date Deposited: | 25 Sep 2010 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1525 |
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