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

Abstract

The study of certain union $X(\mu, b)$ 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 $\dim X(\mu, b)$ for sufficiently large dominant coweight $\mu$.