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arXiv · 1811.11159

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

Rong Zhou·Yihang Zhu
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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.

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BibTeXRIS

Rong Zhou, Yihang Zhu. 2018-11-27. Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties. https://doi.org/10.4310/cjm.2020.v8.n1.a3

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