Affine Deligne–Lusztig varieties and folded galleries governed by chimneys

Document Type

Journal Article

Role

Author

Published In

Annales de l'Institut Fourier

Publisher

Université Grenoble Alpes

Volume

73

Issue

6

First Page

2469

Last Page

2541

Publication Date

10-26-2023

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

Keywords

Affine Deligne–Lusztig variety, positively folded gallery, chimney retraction

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