Eva Viehmann: Dimensions of Affine Deligne-Lusztig varieties
Eva Viehmann
Dimensions of affine Deligne-Lusztig varieties in the affine flag variety – a favorable case
Affine Deligne-Lusztig varieties are locally closed subschemes of the affine flag variety of a reductive group G that are associated with an element x of the affine Weyl group of G and an element b of the loop group of G. They play an important role in the description of the special fiber of Shimura varieties and are an analog and a generalization of the famous Deligne-Lusztig varieties in (classical) flag varieties. However, so far we know very little about their geometry, except in the so-called basic case. In this talk I want to give a short introductory overview of affine Deligne-Lusztig varieties. Then I will discuss a group-theoretic condition on the element x (called cordiality) that allows to determine non-emptiness and to compute the dimension of all affine Deligne-Lusztig varieties for this x and all b, and further implications on the geometry of the Newton stratification.
This is joint work in progress with E. Milicevic.