2003/03/12 by Daniel C. Reuman
Mathematics · #math.RT #msc:20G25
published as Michigan Math. J. 52 (2004), 435-451 · 16 pages, 10 figures
arxiv created 2003/03/12 · arxiv updated 2009/11/30
Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties X_wP(bσ) of a quasisplit connected reductive group G over F = \mathbbFq((t)) for a parahoric subgroup P. They asked which pairs (b, w) give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for P=I an Iwahori subgroup, in the cases b=1, G=SL2, SL3, Sp4. This information is used to get a formula for the dimensions of the X_wK(σ) (all shown to be non-empty by Rapoport and Kottwitz) for the above G that supports a general conjecture of Rapoport. Here K is a special maximal compact subgroup.