# zbMATH — the first resource for mathematics

The closure diagram for nilpotent orbits of the real form EIX of $$E_ 8$$. (English) Zbl 1033.17012
Let $${\mathfrak O}_1$$ and $${\mathfrak O}_2$$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write $${\mathfrak O}_1 \geq {\mathfrak O}_2$$ if $${\mathfrak O}_2$$ is contained in the closure of $${\mathfrak O}_1$$. This defines a partial order on the set of such orbits, known as the closure ordering. In this paper, the author determines this order for the noncompact nonsplit real form of the simple complex Lie algebra $$E_8$$. The closure diagrams for adjoint nilpotent orbits in noncompact real form of $$F_4$$, $$G_2$$, $$E_6$$ were determined by the author in [ J. Lie Theory 10, 491–510 (2000; Zbl 0974.17010)], and for the noncompact and nonsplit real forms of $$E_7$$ in [ Represent. Theory 5, 17–42 (2001; Zbl 1031.17004)].

##### MSC:
 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B20 Simple, semisimple, reductive (super)algebras 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
##### Keywords:
closure diagram; nilpotent orbit; real form
Full Text: