Dimension formula of the affine Deligne-Lusztig variety $X(μ, b)$

Abstract

The study of certain union X(µ, b) of affine Deligne-Lusztig varieties in the affine flag varieties arose from the study of Shimura varieties with Iwahori level structure. In this paper, we give an explicit formula of dim X(µ, b) for sufficiently large dominant coweight µ.