  We study the PBW filtration on the irreducible highest weight representations
of simple complex finite-dimensional Lie algebras. This filtration is induced
by the standard degree filtration on the universal enveloping algebra. For
certain rectangular weights we provide a new description of the associated
graded module in terms of generators and relations. We also construct a basis
parametrized by the integer points of a normal polytope. The main tool we use
is the Hasse diagram defined via the standard partial order on the positive
roots. As an application we conclude that all representations considered in
this paper are Feigin-Fourier-Littelmann modules.
