Lie algebras associated with a standard quadruplet and prehomogeneous vector spaces

Abstract

By using the theory of Lie algebras associated with a standard quadruplet, we can embed an arbitrary reductive prehomogeneous vector space with completely reducible representation into some graded Lie algebra. The purpose of this paper is to study properties of graded Lie algebras which correspond to the prehomogeneity condition of triplets. Moreover, we give another proof of castling transformation as an application.