Affine Deligne-Lusztig varieties in affine flag varieties

Abstract

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.

44 pages, 4 figures. Minor changes to font, references, and acknowledgments. Improved introduction, other improvements in exposition, and two new figures added, for a total of 4