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


Author: J. J. Duistermaat
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1983-0678361-2
Article copyright: © Copyright 1983 American Mathematical Society

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