On the conjugacy of maximal unipotent subgroups of real semisimple Lie groups

Abstract

The existence of closed orbits of real algebraic groups on real algebraic varieties is established. As an application, it is shown that if G is a real reductive linear group with Iwasawa decomposition G= KAN, then every unipotent subgroup of G is conjugate to a subgroup of N.

This supersedes 1112.5468. Final version; to appear in Journal of Lie-Theory