STRATIFICATIONS OF AFFINE DELIGNE-LUSZTIG VARIETIES

Affine Deligne-Lusztig varieties are analogues of Deligne-Lusztig varieties in the context of affine flag varieties and affine Grassmannians. They are closely related to moduli spaces of p-divisible groups in positive characteristic and thus to arithmetic properties of Shimura varieties. We compare stratifications of affine Deligne-Lusztig varieties attached to a basic element b. In particular, we show that the stratification defined by Chen and Viehmann using the relative position to elements of the group J(b), the sigma-centralizer of b, coincides with the Bruhat-Tits stratification in all cases of Coxeter type, as defined by X. He and the author.