Symplectic homogeneous spaces

Sternberg, Shlomo

doi:10.1090/S0002-9947-1975-0379759-8

Symplectic homogeneous spaces
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by Shlomo Sternberg

Trans. Amer. Math. Soc. 212 (1975), 113-130

DOI: https://doi.org/10.1090/S0002-9947-1975-0379759-8

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Abstract:

In this paper we make various remarks, mostly of a computational nature, concerning a symplectic manifold X on which a Lie group G acts as a transitive group of symplectic automorphisms. The study of such manifolds was initiated by Kostant [4] and Souriau [5] and was recently developed from a more general point of view by Chu [2]. The first part of this paper is devoted to reviewing the Kostant, Souriau, Chu results and deriving from them a generalization of the Cartan conjugacy theorem. In the second part of this paper we apply these results to Lie algebras admitting a generalized (k, p) decomposition.

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