Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Isotropy Representation of a Real Flag Manifold: Split Real Forms   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.

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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th