Stabilizers of irreducible components of affine Deligne–Lusztig varieties
Xuhua He
The University of Hong Kong, P.R. ChinaRong Zhou
University of Cambridge, UKYihang Zhu
Tsinghua University, Beijing, P.R. China
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Abstract
We study the -action on the set of top-dimensional irreducible components of affine Deligne–Lusztig varieties in the affine Grassmannian. We show that the stabilizer of any such component is a parahoric subgroup of of maximal volume, verifying a conjecture of X. Zhu. As an application, we give a description of the set of top-dimensional irreducible components in the basic locus of Shimura varieties.
Cite this article
Xuhua He, Rong Zhou, Yihang Zhu, Stabilizers of irreducible components of affine Deligne–Lusztig varieties. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1414