Stabilizers of irreducible components of affine Deligne–Lusztig varieties

Xuhua He; Rong Zhou; Yihang Zhu

doi:10.4171/jems/1414

JournalsjemsVol. 27, No. 6pp. 2387–2441

Stabilizers of irreducible components of affine Deligne–Lusztig varieties

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

Download PDF

This article is published open access under our Subscribe to Open model.

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. 27 (2025), no. 6, pp. 2387–2441

DOI 10.4171/JEMS/1414