A remark on the regularity of prehomogeneous vector spaces

Abstract

In this note, we prove that if $(G,V)$ is a prehomogeneous vector space over any field $k$ such that the stabilizer of a generic point is reductive, the set of semi-stable points is a single orbit over the separable closure of $k$.

Cited by in corpus (3)

• Rational orbits of the space of pairs of exceptional Jordan algebras
• On equivariant maps related to the space of pairs of exceptional Jordan algebras
• On parameterizations of rational orbits of some forms of prehomogeneous vector spaces