Irreducible components of affine Deligne–Lusztig varieties

Abstract

By extending the method of semi-modules developed by de Jong,Oort, Viehmann and Hamacher, we introduce a stratification for the affine Deligne-Lusztig variety (in the affine Grassmannian) attached to a basic element. As an application, we verify a conjecture, due to M. Chen and X. Zhu, on the irreducible components of the affine Deligne-Lusztig variety attached to a sum of dominant minuscule coweights.