The PBW filtration and convex polytopes in type
arXiv:1504.06522
Abstract
We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type . We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional representations for , that there exists a normal polytope such that the lattice points of this polytope parametrize a basis of the corresponding associated graded space. As a consequence we obtain several classes of favourable modules and graded combinatorial character formulas.