Affine Deligne–Lusztig varieties associated to additive affine Weyl group elements
Journal of Algebra
This work provides a partial proof of a conjecture of Goertz, Haines, Kottwitz, and Reuman predicting non-emptiness of affine Deligne-Lusztig varieties. The method of proof generalizes an argument in the original paper of Deligne and Lusztig in the Annals of Mathematics. Many intricate arguments involving the combinatorics of Coxeter groups are also employed.
"Affine Deligne-Lusztig varieties associated to additive affine Weyl group elements," J. Algebra 349, no. 1, p. 63-79, 2012.