Cambridge Journal of Mathematics

Volume 10 (2022)

Number 2

Irreducible components of affine Deligne–Lusztig varieties

Pages: 433 – 510

DOI: https://dx.doi.org/10.4310/CJM.2022.v10.n2.a2

Author

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)

Abstract

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.

Keywords

affine Deligne–Lusztig varieties, Mirković–Vilonen cycles

2010 Mathematics Subject Classification

Primary 20G25. Secondary 14G35.

Full Text (PDF format)

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