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

Duistermaat, J. J.

doi:10.1090/S0002-9947-1983-0678361-2

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 $Q$.

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