Equivariant compactifications of a nilpotent group by $G/P$

Abstract

Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$ and $N$ the unipotent radical of $P.$ The so-called equivariant compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a dense open orbit isomorphic to $N$. In this article, we investigate how many such equivariant compactifications there exist. Our result says that there is a unique equivariant compactification of $N$ by $G/P$, up to isomorphism, except ${\P }^n$.

20 pages, to appear in Transformation Groups

References in corpus (1)

• On automorphism groups of some types of generic distributions

Cited by in corpus (3)

• Radiant toric varieties and unipotent group actions
• Euler-symmetric complete intersection in projective space
• ${\mathbb{H}}_{2n+1}$-structures on odd dimensional projective spaces