Convexity properties of gradient maps |
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Authors: | Peter Heinzner |
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Institution: | a Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany b Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany |
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Abstract: | We consider the action of a real reductive group G on a Kähler manifold Z which is the restriction of a holomorphic action of a complex reductive group H. We assume that the action of a maximal compact subgroup U of H is Hamiltonian and that G is compatible with a Cartan decomposition of H. We have an associated gradient map μp:Z→p where g=k⊕p is the Cartan decomposition of g. For a G-stable subset Y of Z we consider convexity properties of the intersection of μp(Y) with a closed Weyl chamber in a maximal abelian subspace a of p. Our main result is a Convexity Theorem for real semi-algebraic subsets Y of Z=P(V) where V is a unitary representation of U. |
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Keywords: | Hamiltonian actions Actions of real forms Convexity of momentum map |
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