## Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution

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- by J. J. Duistermaat PDF
- Trans. Amer. Math. Soc.
**275**(1983), 417-429 Request permission

## Abstract:

The Kostant convexity theorem for real flag manifolds is generalized to a Hamiltonian framework. More precisely, it is proved that if $f$ is the momentum mapping for a Hamiltonian torus action on a symplectic manifold $M$ and $Q$ is the fixed point set of an antisymplectic involution of $M$ leaving $f$ invariant, then $f(Q) = f(M) =$ a convex polytope. Also it is proved that the coordinate functions of $f$ are tight, using "half-turn" involutions of $Q$.## References

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## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**275**(1983), 417-429 - MSC: Primary 53C15; Secondary 55M20, 58F05
- DOI: https://doi.org/10.1090/S0002-9947-1983-0678361-2
- MathSciNet review: 678361