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

  • Ulrich Görtz

  • Xuhua He

    9 Clear Water Bay 45326 Essen Kowloon Germany Hong Kong
Dimensions of affine Deligne-Lusztig varieties in affine flag varieties. cover
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Abstract

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 [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic -conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic -conjugacy class is the class of , we also prove the dimension formula predicted in op. cit. in almost all cases.

Cite this article

Ulrich Görtz, Xuhua He, Dimensions of affine Deligne-Lusztig varieties in affine flag varieties.. Doc. Math. 15 (2010), pp. 1009–1028

DOI 10.4171/DM/322