The closure diagram for nilpotent orbits of the split real form of \(E_8\)

DOI10.2478/BF02475183zbMath1050.17006OpenAlexW2113011496MaRDI QIDQ1419667

Dragomir Ž. Djoković

Publication date: 19 January 2004

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/bf02475183

zbMATH Keywords

prehomogeneous vector spacesadjoint actionexceptional Lie groupsclosures of nilpotent orbitsKostant-Sekiguchi bijectionnormal triples

Mathematics Subject Classification ID

Exceptional (super)algebras (17B25) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40)

Related Items (7)

Octonionic black holes ⋮ Extremal black holes, nilpotent orbits and the true fake superpotential ⋮ An effective method to compute closure ordering for nilpotent orbits of \(\theta \)-representations ⋮ Corrections for ``The closure diagram for nilpotent orbits of the split real form of \(E_ 8\) ⋮ Orbit closure diagram for the space of quadruples of quinary alternating forms ⋮ Equivariant deformation quantization and coadjoint orbit method ⋮ Irreducible components of the nilpotent commuting variety of a symmetric semisimple Lie algebra

Uses Software

• Maple
• LiE

Cites Work

• The closure diagram for nilpotent orbits of the real form EIX of \(E_ 8\).
• Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\)
• Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers
• The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
• Explicit Cayley triples in real forms of \(G_2\), \(F_4\), and \(E_6\)
• Explicit Cayley triples in real forms of \(E_8\)
• The closure diagrams for nilpotent orbits of the real forms EVI and EVII of 𝐄₇
• The closure diagram for nilpotent orbits of the split real form of 𝐸₇
• Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• Closure ordering and the Kostant-Sekiguchi correspondence
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