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On affine Weyl group elements of positive Coxeter type
Published 5 Dec 2023 in math.AG and math.RT | (2312.02630v3)
Abstract: We introduce a class of elements of the Iwahori-Weyl group of a reductive group that we call positive Coxeter elements. This class consists of elements which are linked to partial Coxeter elements in the finite Weyl group in a certain canonical way, extending the more restrictive notion of finite Coxeter part previously introduced by He-Nie-Yu. We show that the affine Deligne-Lusztig varieties associated with such elements have a very simple and explicitly described geometric structure. Conversely, we explain how some of these geometric properties can be used to characterize elements of positive Coxeter type.
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