Journal of Noncommutative Geometry
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Published online: 2010-03-02
R-groups and geometric structure in the representation theory of SL(N)Jamila Jawdat and Roger Plymen (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 .
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