The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This survey deals with recent progress on several important problems on affine Deligne-Lusztig varieties. The emphasis is on the Lie-theoretic aspect, while some connections and applications to arithmetic geometry will also be mentioned.
Xuhua He. Some results on affine Deligne-Lusztig varieties. 2018. In arXiv preprint arXiv:1807.02158. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113050376727789.