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Journal of Lie Theory, Vol. 10, No. 2, pp. 491-510 (2000)
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The closure diagrams for nilpotent orbits of real forms of F$_4$ and G$_2$

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Dragomir Z. Djokovic

Department of Pure Mathematics

University of Waterloo

Waterloo, Ontario, Canada N2L 3G1

dragomir@herod.uwaterloo.ca

**Abstract:** Let ${\cal O}_1$ and ${\cal O}_2$ be two adjoint nilpotent orbits in a real semisimple Lie algebra $\g_0$. We shall write ${\cal O}_1 \geq {\cal O}_2$ if ${\cal O}_2$ is contained in the closure of ${\cal O}_1$. This defines a partial order on the set of such orbits and we refer to this order as the closure ordering. We determine the closure ordering for adjoint nilpotent orbits when $\g_0$ is of type G$ $I, F$ $I, or F$ $II. The cases G$ $I and F$ $II are rather trivial and are included only for the sake of completeness.

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