Non-parabolic prehomogeneous vector spaces and exceptional Lie algebras

Among the classification of irreducible regular and reduced prehomogeneous vector spaces, there are only a few one which are not of parabolic type. In this paper we investigate this family of prehomogeneous vector and show that they nevertheless all occur inside the exceptional Lie algebras and are in some sense close to the parabolic family. Moreover we give a Lie theoretical description of their relative invariants and the corresponding characters.