Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 616 页 · Chapter X，Section 1「Definitions and Examples」
Let $G$ be a connected complex Lie group; usually we shall assume that $G$ is the complexification of a compact Lie group $U$. A prehomogeneous vector space for $G$ is a complex finite-dimensional vector space $V$ together with a holomorphic representation of $G$ on $V$ such that $G$ has an open orbit in $V$.