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](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-15.png&w=3840&q=90)
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