The Isotropy Representation of a Real Flag Manifold: Split Real Forms

2014/05/26 by Mauro Patrão, Patrão, Mauro, Luiz A. B. San Martin +1
Mathematics · #14M15 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:14M15

paper · pdf · doi:10.48550/arxiv.1405.6561

arxiv created 2014/05/26 · arxiv updated 2014/05/27

Abstract

We study the isotropy representation of real flag manifolds associated to simple Lie algebras that are split real forms of complex simple Lie algebras. For each Dynkin diagram the invariant irreducible subspaces for the compact part of the isotropy subgroup are described. Contrary to the complex flag manifolds the decomposition into irreducible components is not in general unique, since there are cases with infinitely many invariant subspaces.

Related

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• Invariant Einstein metrics on real flag manifolds with two or three isotropy summands
• Classical Symmetries of Complex Manifolds
• Orbits of real forms in complex flag manifolds
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