Orbits of Real Algebraic Groups
  The existence of closed orbits of real algebraic groups on certain real algebraic spaces is established. As an application it is shown that if $G$ is a real reductive group with Iwasawa decomposition $G=KAN$, then all unipotent subgroups of $G$ are conjugate to a subgroup of $N$. 
H. Azad
math.GR math-ph math.MP