Affine Deligne-Lusztig varieties
The preprint "Affine Deligne-Lusztig varieties and folded galleries governed by chimneys" by Elizabeth Milićević, Petra Schwer and Anne Thomas has recently been uploaded to the arXiv!
Link to the paper: arXiv:2006.16288.
Abstract:
We characterize the nonemptiness and dimension problems for an affine Deligne-Lusztig variety \(X_x(b)\) in the affine flag variety in terms of galleries that are positively folded with respect to a chimney. If the parabolic subgroup associated to the Newton point of \(b\) has rank 1, we then prove nonemptiness for a certain class of Iwahori-Weyl group elements \(x\) by explicitly constructing such galleries.