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

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

2006-12-11

arxiv.org/abs/math/0612273v5

Mathematics

K-Theory and Homology

16 pages. Final version, to be published in the Journal of Noncommutative Geometry

Scientific paper

Let $F$ be a nonarchimedean local field of characteristic zero and let 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 [3].

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