Stabilizers of irreducible components of affine Deligne–Lusztig varieties

Xuhua He; Rong Zhou; Yihang Zhu

doi:10.4171/jems/1414

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Stabilizers of irreducible components of affine Deligne–Lusztig varieties

Xuhua He
The University of Hong Kong, P.R. China
Rong Zhou
University of Cambridge, UK
Yihang Zhu
Tsinghua University, Beijing, P.R. China

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Abstract

We study the $J_{b} (F)$ -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 $J_{b} (F)$ 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