Abstract:We investigate Hamiltonian actions of non-compact Lie groups on a homogeneous bounded domain $X$. As a main result, we point out a Lie-theoretical condition for a closed Lie group $H$ of the automorphism group of $X$ which ensures that the symplectic reduction $\mu^{-1}(0)/H$ with respect to the momentum map $\mu$ at hand, is a Stein manifold. Moreover, for the class of connected subgroups of translations the quotient $(H^\mathbb{C}\cdot X)/H^\mathbb{C}$ is realized as a Siegel domain and we show that the symplectic reduction $\mu^{-1}(0)/H$ is biholomorphic to such a Stein quotient.
From: Maxim Kukol [view email]
[v1]
Tue, 23 Sep 2025 17:55:53 UTC (17 KB)
[v2]
Wed, 24 Jun 2026 09:54:29 UTC (16 KB)
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