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2010.84: Geometric structure in the tempered dual of SL(N)

2010.84: Kuok Fai Chao (2010) Geometric structure in the tempered dual of SL(N). PhD 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 (PhD)
Uncontrolled Keywords:Representation theory, special linear group
Subjects:MSC 2000 > 11 Number theory
MSC 2000 > 22 Topological groups, Lie groups
MIMS number:2010.84
Deposited By:Professor Roger Plymen
Deposited On:25 September 2010

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