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Journal of Noncommutative Geometry


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Volume 4, Issue 2, 2010, pp. 265–279
DOI: 10.4171/JNCG/55

Published online: 2010-03-02

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

Jamila Jawdat[1] and Roger Plymen[2]

(1) Zarqa Private University, Jordan
(2) Manchester University, UK

Let F be a nonarchimedean local field of characteristic zero and let G = 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 [2].

Keywords: Local field, special linear group, elliptic representations, L-packets, K-theory, reduced C*-algebra

Jawdat Jamila, Plymen Roger: R-groups and geometric structure in the representation theory of SL(N). J. Noncommut. Geom. 4 (2010), 265-279. doi: 10.4171/JNCG/55