Hamiltonian Actions on Homogeneous Bounded Domains

2025/09/23 by Kukol, Maxim
#Complex Variables (math.CV) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2509.19293

Abstract

This paper examines Hamiltonian actions of non-compact Lie groups on homogeneous bounded domains X in 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^ℂ⋅ X)/H^ℂ is a Stein manifold and the symplectic reduction μ^-1(0)/H is biholomorphic to this quotient.

Citations

• Invariant Kähler potentials and symplectic reduction
• Equivariant Kählerian extensions of contact manifolds
• Cartan decomposition of the moment map
• The extended future tube conjecture for SO(1,n)
• The minimum principle from a Hamiltonian point of view
• Geometric quantization and multiplicities of group representations

Related

• Hamiltonian actions and Lagrangian homogeneous submanifolds
• Hamiltonian group actions on exact symplectic manifolds with proper momentum maps are standard
• On cohomology of invariant submanifolds of Hamiltonian actions
• Special Hamiltonian S¹-actions on symplectic 4-manifolds
• Abelian instances of nonabelian symplectic reduction