 Prehomogeneous vector space

In mathematics, a prehomogeneous vector space (PVS) is a finite-dimensional vector space "V" together with a subgroup "G" of the general linear group GL("V") such that "G" has an open dense orbit in "V".Prehomogeneous vector spaces were introduced by Mikio Sato in 1970 and have many applications in geometry, number theory and analysis, as well as representation theory.