Conformal actions on the Einstein universe

Abstract

In this paper we study nontransitive irreducible and transitive reducible conformal actions on the Einstein universe Ein1,n−1. In either case, we give the explicit representation of the acting group in O(2,n). When the action is nontransitive and irreducible, we determine the dimension and the causal character of the induced orbits in the nullcone of R2,n and then in the Einstein universe. We prove that any such nontransitive action induces an open orbit in the Einstein universe and that the orbit space is finite.