The minimum principle from a Hamiltonian point of view

  • Peter Heinzner

    Brandeis University Department of Mathematics Waltham, MA 02254-9110, USA
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Abstract

Let GG be a complex Lie group and GRG_\R a real form of GG. For a GRG_\R-stable domain of holomorphy XX in a complex GG-manifold we consider the question under which conditions the extended domain GXG\cdot X is a domain of holomorphy. We give an answer in term of GRG_\R-invariant strictly plurisubharmonic functions on XX and the associate Marsden-Weinstein reduced space which is given by the Kaehler form and the moment map associated with the given strictly plurisubharmonic function. Our main application is a proof of the so called extended future tube conjecture which asserts that GXG\cdot X is a domain of holomorphy in the case where XX is the NN-fold product of the tube domain in \C4\C^4 over the positive light cone and GG is the connected complex Lorentz group acting diagonally.

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Peter Heinzner, The minimum principle from a Hamiltonian point of view. Doc. Math. 3 (1998), pp. 1–14

DOI 10.4171/DM/36