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

Dragomir Đoković

Open Mathematics, Tome 1 (2003), p. 573-643 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $𝒪_{1}$ and $𝒪_{2}$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write $𝒪_{1}$ ≥ $𝒪_{2}$ if $𝒪_{2}$ is contained in the closure of $𝒪_{1}$ . 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 $\partial 𝒪_{1}^{i}$ and of the intersections $\bar{𝒪_{l}^{i}} \cap \bar{𝒪_{l}^{j}}$ .

Publié le : 2003-01-01

Zbl 1050.17006

EUDML-ID : urn:eudml:doc:268838

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     author = {Dragomir \DJ okovi\'c},
     title = {The closure diagram for nilpotent orbits of the split real form of E8},
     journal = {Open Mathematics},
     volume = {1},
     year = {2003},
     pages = {573-643},
     zbl = {1050.17006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475183}
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Dragomir Đoković. The closure diagram for nilpotent orbits of the split real form of E8. Open Mathematics, Tome 1 (2003) pp. 573-643. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475183/

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