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

摘要

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