Cambridge Journal of Mathematics
Volume 8 (2020)
Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties
Pages: 149 – 241
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 Mirković–Vilonen basis of a certain weight space of a representation of the Langlands dual group.
twisted orbital integrals, affine Deligne–Lusztig varieties
2010 Mathematics Subject Classification
Primary 11G18. Secondary 22E35.
R. Z. is partially supported by NSF grant DMS-1638352 through membership at the Institute for Advanced Study.
Y. Z. is supported by NSF grant DMS-1802292.
Received 27 December 2018
Published 25 February 2020