  Let G be a connected reductive complex algebraic group and B a Borel subgroup
of G. We consider a subgroup H of B acting with finitely many orbits on the
flag variety G/B, and we classify the H-orbits in G/B in terms of suitable
combinatorial invariants. As well, we study the Weyl group action defined by
Knop on the set of H-orbits in G/B, and we give a combinatorial model for this
action in terms of weight polytopes.
