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Polar orthogonal representations of real reductive algebraic groups

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
320
Issue
7
Identifiers
DOI: 10.1016/j.jalgebra.2008.06.027
Keywords
  • Polar Representations
  • Real Reductive Algebraic Groups
  • Pseudo-Riemannian Symmetric Spaces
Disciplines
  • Mathematics

Abstract

Abstract We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras.

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