 The irreducible PVS were classified by Sato and Tatsuo Kimura in 1977, up to a transformation known as "castling".They are subdivided into two types, according to whether the semisimple part of "G" acts prehomogeneously or not.If it doesn't then there is a homogeneous polynomial on "V" which is invariant under the semisimple part of "G".