Dimensions of affine Deligne-Lusztig varieties in affine flag varieties.
Xuhua He9 Clear Water Bay 45326 Essen Kowloon Germany Hong Kong
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  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. 1009–1028DOI 10.4171/DM/322