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Connected components of closed affine Deligne–Lusztig varieties

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Abstract

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.

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  1. Mathematisches Institut der Universität Bonn, Beringstrasse 1, 53115, Bonn, Germany

    Eva Viehmann

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  1. Eva Viehmann
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Correspondence to Eva Viehmann.

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Viehmann, E. Connected components of closed affine Deligne–Lusztig varieties. Math. Ann. 340, 315–333 (2008). https://doi.org/10.1007/s00208-007-0153-8

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  • DOI: https://doi.org/10.1007/s00208-007-0153-8

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