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Stabilizers of irreducible components of affine Deligne--Lusztig varieties

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arxiv 2109.02594 v1 pith:PQSGAPTV submitted 2021-09-06 math.AG math.NT

Xuhua He , Rong Zhou , Yihang Zhu This is my paper · ORCID
classification math.AGmath.NT
keywords affinecomponentsirreduciblevarietiesdeligne--lusztigtop-dimensionalactionapplication
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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.

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