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The closure diagrams for nilpotent orbits of the real forms EVI and EVII of \(\mathbf{E}_7\). (English) Zbl 1031.17004
Summary: Let \(\mathcal{O}_1\) and \(\mathcal{O}_2\) be adjoint nilpotent orbits in a real semisimple Lie algebra. Write \(\mathcal{O}_1\geq\mathcal{O}_2\) if \(\mathcal{O}_2\) is contained in the closure of \(\mathcal{O}_1.\) This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the two noncompact nonsplit real forms of the simple complex Lie algebra \(E_7.\)

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
Software:
Maple; LiE
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