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

Rong Zhou Imperial College London Yihang Zhu Columbia University

Number Theory Representation Theory Algebraic Geometry mathscidoc:2005.24005

Gold Award Paper in 2020

Cambridge Journal of Mathematics, 8, (1), 2020.2
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 σ-centralizer group to the Mirkovic-Vilonen basis of a certain weight space of a representation of the Langlands dual group.
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@inproceedings{rong2020twisted,
  title={Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties},
  author={Rong Zhou, and Yihang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200518073919339328685},
  booktitle={Cambridge Journal of Mathematics},
  volume={8},
  number={1},
  year={2020},
}
Rong Zhou, and Yihang Zhu. Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties. 2020. Vol. 8. In Cambridge Journal of Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200518073919339328685.
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