Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties Article Swipe

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Mathematics Langlands dual group Pure mathematics Centralizer and normalizer Affine transformation Modulo Conjecture Weyl group Algebra over a field Combinatorics

Zhou Rong , Yihang Zhu ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.4310/cjm.2020.v8.n1.a3 · OA: W2902135339

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.