Displaying similar documents to “Algorithmic orbit classification for some Borel group actions”

On spherical nilpotent orbits and beyond

Dmitri I. Panyushev (1999)

Annales de l'institut Fourier

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We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s θ -groups. This yields a description...

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

Dragomir Đoković (2003)

Open Mathematics

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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...