# Dimensions of affine Deligne-Lusztig varieties in affine flag varieties

Ulrich Goertz, Xuhua He

Number | 10 |
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Author | Ulrich Goertz |

Year | 2010 |

Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper arXiv:0805.0045v4 by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic \sigma-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic \sigma-conjugacy class is the class of b=1, we also prove the dimension formula predicted in op. cit. in almost all cases.