The Closure Diagrams for Nilpotent Orbits of Real Forms of E$_ 6$

Abstract: Let ${\cal O}_1$ and ${\cal O}_2$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write ${\cal O}_1\geq{\cal O}_2$ if ${\cal O}_2$ is contained in the closure of ${\cal O}_1.$ This gives a partial order on the set of such orbits, which is known as the closure ordering. We determine this ordering for the adjoint nilpotent orbits of the four noncompact real forms of the simple complex Lie algebra $E_6.$

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