Torus orbit closures in the flag variety

Abstract

The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand-Serganova in the mid-1980s, but it seems that not much has been done since then. In this chapter, we present some of the work by Klyachko and Gelfand-Serganova and our recent work on the topology, geometry, and combinatorics of torus orbit closures in the flag variety.