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We introduce a class of elements of the Iwahori-Weyl group of a reductivegroup that we call positive Coxeter elements. This class consists of elementswhich are linked to partial Coxeter elements in the finite Weyl group in acertain canonical way, extending the more restrictive notion of finite Coxeterpart previously introduced by He-Nie-Yu. We that the affine Deligne-Lusztigvarieties associated with such elements have a very simple and explicitlydescribed geometric structure. Conversely, we explain how some of thesegeometric properties can be used to characterize elements of positive Coxetertype.

On affine Weyl group elements of positive Coxeter type