Geometric structure in the tempered dual of SL(N)

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: http://eprints.maths.manchester.ac.uk/id/eprint/1525

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