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arXiv · 2006.16288

Affine Deligne-Lusztig varieties and folded galleries governed by chimneys

Elizabeth Milićević·Petra Schwer·Anne Thomas
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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.

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Elizabeth Milićević, Petra Schwer, Anne Thomas. 2020-06-29. Affine Deligne-Lusztig varieties and folded galleries governed by chimneys. https://arxiv.org/abs/2006.16288

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