A classification of irreducible prehomogeneous vector spaces and their relative invariants

Let G be a connected linear algebraic group, and p a rational representation of G on a finite-dimensional vector space V , all defined over the complex number field C . We call such a triplet ( G, p, V ) a prehomogeneous vector space if V has a Zariski-dense G -orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces when p is irreducible, and to investigate their relative invariants and the regularity.