Let be a complex Lie group and a real form of . For a -stable domain of holomorphy in a complex -manifold we consider the question under which conditions the extended domain is a domain of holomorphy. We give an answer in term of -invariant strictly plurisubharmonic functions on 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 is a domain of holomorphy in the case where is the -fold product of the tube domain in over the positive light cone and 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. 1–14DOI 10.4171/DM/36