Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties

Abstract

We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition functions. As an application we prove a conjecture of Miaofen Chen and Xinwen Zhu, relating the set of irreducible components of an affine Deligne-Lusztig variety modulo the action of the $\sigma$-centralizer group to the Mirkovic-Vilonen basis of a certain weight space of a representation of the Langlands dual group.

arXiv commentFinal, published version

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Cited by in corpus (4)

• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits
• Geometric Structure of Affine Deligne-Lusztig Varieties for $G{L}_3$
• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)