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Mathematische Annalen

, Volume 317, Issue 3, pp 415–457 | Cite as

Moment maps and Riemannian symmetric pairs

  • Luis O'Shea
  • Reyer Sjamaar
Original article

Abstract.

We study Hamiltonian actions of a compact Lie group on a symplectic manifold in the presence of an involution on the group and an antisymplectic involution on the manifold. The fixed-point set of the involution on the manifold is a Lagrangian submanifold. We investigate its image under the moment map and conclude that the intersection with the Weyl chamber is an easily described subpolytope of the Kirwan polytope. Of special interest is the integral Kähler case, where much stronger results hold. In particular, we obtain convexity theorems for closures of orbits of the noncompact dual group (in the sense of the theory of symmetric pairs). In the abelian case these results were obtained earlier by Duistermaat. We derive explicit inequalities for polytopes associated with real flag varieties.

Keywords

Manifold Special Interest Symplectic Manifold Strong Result Dual Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Luis O'Shea
    • 1
  • Reyer Sjamaar
    • 1
  1. 1.Department of Mathematics, Cornell University, Ithaca, New York 14853-7901 (e-mail: {luis,sjamaar}@math.cornell.edu) US

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