Formulas for the dimensions of some affine Deligne-Lusztig Varieties
نویسنده
چکیده
Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties X w̃ (bσ) of a quasisplit connected reductive group G over F = Fq((t)) for a parahoric subgroup P . They asked which pairs (b, w̃) 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 w̃ (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
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