Cambridge Journal of Mathematics

Volume 10 (2022)

Number 2

Irreducible components of affine Deligne–Lusztig varieties

Pages: 433 – 510



Sian Nie (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, China)


We determine the top-dimensional irreducible components (and their stabilizers in the Frobenius twisted centralizer group) of affine Deligne–Lusztig varieties in the affine Grassmannian of a reductive group, by constructing a natural map from the set of irreducible components to the set of Mirković–Vilonen cycles. This in particular verifies a conjecture by Miaofen Chen and Xinwen Zhu.


affine Deligne–Lusztig varieties, Mirković–Vilonen cycles

2010 Mathematics Subject Classification

Primary 20G25. Secondary 14G35.

This work is partially supported by the National Key R&D Program of China, No. 2020YFA0712600, and the National Natural Science Foundation of China No. 11922119 and No. 12288201.

Received 15 May 2021

Published 23 June 2022