Hamiltonian Actions on Homogeneous Bounded Domains

Fuente: arXiv
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Main Author: Kukol, Maxim
Format: Preprint
Published: 2025
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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