Divided difference operators on polytopes

Abstract

We define convex-geometric counterparts of divided difference (or Demazure) operators from the Schubert calculus and representation theory. These operators are used to construct inductively polytopes that capture Demazure characters of representations of reductive groups. In particular, Gelfand–Zetlin polytopes and twisted cubes of Grossberg–Karshon are obtained in a uniform way.