Intersections of Deligne--Lusztig varieties and Springer fibres
arXiv:2101.00537
Abstract
In this paper we prove a direct geometric relation between Deligne--Lusztig varieties and Springer fibres in type : For any rational unipotent element, the Springer fibre cuts out a unique component of a specific Deligne--Lusztig variety; moreover, this component forms an open dense subset of a component of the Springer fibre. This boils down to a map from the unipotent variety to the Weyl group, and combines several constructions with a combinatorial flavour (like Weyr normal forms, Robinson--Schensted correspondence, and Spaltenstein's and Steinberg's labellings); it also provides a geometric interpretation of a classical dimension formula of unipotent centralisers.
16 pages, comments welcome