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 .
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Jamila Jawdat, Roger Plymen, <var>R</var>-groups and geometric structure in the representation theory of SL(<var>N</var>). J. Noncommut. Geom. 4 (2010), no. 2, pp. 265–279DOI 10.4171/JNCG/55