Prehomogeneous spaces for parabolic group actions in classical groups.

DOI10.1016/J.JALGEBRA.2003.11.005zbMath1064.20048OpenAlexW2044189975MaRDI QIDQ1883065

Gerhard Röhrle, Simon M. Goodwin

Publication date: 1 October 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.11.005

zbMATH Keywords

parabolic subgroupsadjoint actionsdense orbitsprehomogeneous spaces

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Prehomogeneous vector spaces (11S90) Lie algebras of linear algebraic groups (17B45)

Related Items (5)

Finite orbit modules for parabolic subgroups of exceptional groups. ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Richardson elements for classical Lie algebras ⋮ Algorithmic testing for dense orbits of Borel subgroups

Cites Work

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• Linear algebraic groups
• On the modality of parabolic subgroups of linear algebraic groups
• A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical
• The \(\Delta\)-filtered modules without self-extensions for the Auslander algebra of \(k[T/\langle T^n\rangle\)]
• Variation on a theme of Richardson.
• Finite orbit modules for parabolic subgroups of exceptional groups.
• Finite, tame, and wild actions of parabolic subgroups in \(\text{GL}(V)\) on certain unipotent subgroups
• On parabolic subgroups of classical groups with a finite number of orbits on the unipotent radial
• Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups
• Finiteness for parabolic group actions in classical groups.

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