  The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is
closely connected to the topic of prehomogeneous affine representations of Lie
groups. In this article, we exhibit several aspects of this correspondence. At
the heart of our presentation is a development of the theory of characteristic
classes and characters of prehomogeneous affine representations. We give
applications concerning flat affine, as well as Pseudo-Riemannian and
symplectic affine flat manifolds.
