Abstract
Let F be a nonarchimedean local field of characteristic zero and let G = \mathrm{SL}(N) = \mathrm{SL}(N,F) . This article is devoted to studying the influence of the elliptic representations of \mathrm{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 [Aubert, Baum, Plymen (2007)].
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