Geometric Structure of Affine Deligne-Lusztig Varieties for $G{L}_3$

Abstract

In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $G{L}_3$ and $b$ basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.