Racines orthogonales, formes quadratiques et orbites dʹalgèbres de Lie simples graduées

We give a unified orbital decomposition for irreducible, regular, prehomogeneous vector spaces of parabolic type graded by strongly orthogonal roots of same length, with one-dimensional corresponding root space, on a local or global field of characteristic 0, in terms of a class of quadratic forms related to a root system, Weyl action, and the invariants of the prehomogeneous vector spaces.