R-groups and geometric structure in the representation theory of SL(N)

Jawdat, Jamila and Plymen, Roger (2009) R-groups and geometric structure in the representation theory of SL(N). [MIMS Preprint]

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Abstract

Let $F$ be a nonarchimedean local field of characteristic zero and let $SL(N) = SL(N,F)$. This article is devoted to studying the influence of the elliptic representations of $SL(N)$ on the $K$-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the $R$-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in \cite{ABP}.

Item Type: MIMS Preprint
Uncontrolled Keywords: Local fields, special linear group, elliptic representations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
MSC 2010, the AMS's Mathematics Subject Classification > 46 Functional analysis
Depositing User: Professor Roger Plymen
Date Deposited: 09 Oct 2009
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1318

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