Connected components of closed affine Deligne–Lusztig varieties
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- Viehmann, E. Math. Ann. (2008) 340: 315. doi:10.1007/s00208-007-0153-8
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We determine the set of connected components of closed affine Deligne–Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne–Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-dimensional.