Hamiltonian Actions on Homogeneous Bounded Domains

This paper examines Hamiltonian actions of non-compact Lie groups on homogeneous bounded domains $X$ in ${\mathbb{C}}^d$. In the main part, a Lie-theoretical condition for closed subgroups $H$ of the automorphism group of $X$ is described such that the symplectic reduction ${\mu }^{-1}(0)\mathrm{/}H$ for the momentum map $\mu$ is a Stein manifold. Moreover, for another class of closed subgroups it is shown that the quotient $(H^{\mathbb{C}}\cdot X)\mathrm{/}{H}^{\mathbb{C}}$ is a Stein manifold and the symplectic reduction ${\mu }^{-1}(0)\mathrm{/}H$ is biholomorphic to this quotient.