JournalsjemsOnline First

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
Stabilizers of irreducible components of affine Deligne–Lusztig varieties cover
Download PDF

A subscription is required to access this article.

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