Affine Deligne-Lusztig varieties and folded galleries governed by chimneys
Abstract
We characterize the nonemptiness and dimension problems for an affine Deligne-Lusztig variety Xx(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.
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