EQUIVARIANT COMPACTIFICATIONS OF A NILPOTENT GROUP BY G/P

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 for such triples (G, P, N). Our result says that there is a unique equivariant compactification of N by G / P, up to isomorphism, except for a few triples (G, P, N).