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arXiv · 2109.02594

Stabilizers of irreducible components of affine Deligne--Lusztig varieties

Xuhua He·Rong Zhou·Yihang Zhu
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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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Xuhua He, Rong Zhou, Yihang Zhu. 2021-09-06. Stabilizers of irreducible components of affine Deligne--Lusztig varieties. https://arxiv.org/abs/2109.02594

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