  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 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.

Algebraic Geometry;Representation Theory