Series of nilpotent orbits.

Landsberg, J.M.; Manivel, Laurent; Westbury, Bruce W.

Displaying similar documents to “Series of nilpotent orbits.”

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 index of centralizers of elements of reductive Lie algebras.

Charbonnel, Jean-Yves, Moreau, Anne (2010)

Documenta Mathematica

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Prehomogeneous spaces associated with nilpotent orbits in simple real Lie algebras $E_{6 (6)}$ and $E_{6 (- 26)}$ and their relative invariants.

Jackson, Steven Glenn, Noël, Alfred G. (2006)

Experimental Mathematics

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Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

Andrzej Daszkiewicz, Witold Kraśkiewicz, Tomasz Przebinda (2005)

Open Mathematics

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We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual...

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...