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The closure diagram for nilpotent orbits of the split real form of E8

100%

Đoković D.

Open Mathematics

2003

tom 1

nr 4

573-643

Let $$\mathcal{O}_1 $$ and $$\mathcal{O}_2 $$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write $$\mathcal{O}_1 $$ ≥ $$\mathcal{O}_2 $$ 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 split real form of the simple complex Lie algebra, E 8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries $$\partial \mathcal{O}_1^i $$ and of the intersections $$\overline {\mathcal{O}_l^i } \cap \overline {\mathcal{O}_l^j } $$ .

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1 Open Mathematics

1 Đoković D.

1 2003

Wyniki wyszukiwania

The closure diagram for nilpotent orbits of the split real form of E8