Displaying similar documents to “Flag Manifolds”

Isotropy representation of flag manifolds

Alekseevsky, D. V.

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A flag manifold of a compact semisimple Lie group G is defined as a quotient M = G / K where K is the centralizer of a one-parameter subgroup exp ( t x ) of G . Then M can be identified with the adjoint orbit of x in the Lie algebra 𝒢 of G . Two flag manifolds M = G / K and M ' = G / K ' are equivalent if there exists an automorphism φ : G → G such that φ ( K ) = K ' (equivalent manifolds need not be G -diffeomorphic since φ is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all...

Truncated Lie groups and almost Klein models

Georges Giraud, Michel Boyom (2004)

Open Mathematics

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We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G. Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.