Flag Manifolds

D. V. Alekseevsky

Displaying similar documents to “Flag Manifolds”

Bialgebra structures on a real semisimple Lie algebra.

Chloup, Véronique (1995)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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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 $φ : G \to G$ 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...

Branching theorems for semisimple Lie groups of real rank one

M. Welleda Baldoni Silva (1979)

Rendiconti del Seminario Matematico della Università di Padova

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Multicontact vector fields on Hessenberg manifolds.

Ottazzi, A. (2005)

Journal of Lie Theory

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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.