Hamiltonian Actions on Homogeneous Bounded Domains
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916965067522048 |
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| author | Kukol, Maxim |
| author_facet | Kukol, Maxim |
| contents | 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 $μ^{-1}(0)/H$ for the momentum map $μ$ is a Stein manifold. Moreover, for another class of closed subgroups it is shown that the quotient $(H^\mathbb{C}\cdot X)/H^\mathbb{C}$ is a Stein manifold and the symplectic reduction $μ^{-1}(0)/H$ is biholomorphic to this quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Actions on Homogeneous Bounded Domains Kukol, Maxim Symplectic Geometry Complex Variables 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 $μ^{-1}(0)/H$ for the momentum map $μ$ is a Stein manifold. Moreover, for another class of closed subgroups it is shown that the quotient $(H^\mathbb{C}\cdot X)/H^\mathbb{C}$ is a Stein manifold and the symplectic reduction $μ^{-1}(0)/H$ is biholomorphic to this quotient. |
| title | Hamiltonian Actions on Homogeneous Bounded Domains |
| topic | Symplectic Geometry Complex Variables |
| url | https://arxiv.org/abs/2509.19293 |