2004/02/17 by Leonardo Biliotti, Biliotti, Leonardo · 1 citation
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:53C55. #msc:57S15 #primary 53C55. secondary 57S15
paper · pdf · doi:10.48550/arxiv.math/0402277
v1: 7 pages, added refernces and changed content v2: 22 may 2006, 12 pages, completely rewritten
openalex publication_date 2004/02/17 · arxiv created 2006/05/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (M,ω) be a connected symplectic manifold on which a connected Lie group G acts properly and in a Hamiltonian fashion with moment map μ:M \lra \mf g^*. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete classification of multiplicity-free actions of compact Lie groups acting isometrically and in a Hamiltonian fashion on Hermitian symmetric spaces of noncompact type. Successively we make a connection between multiplicity-free actions on M and multiplicity-free actions on the symplectic reduction and on the symplectic cut, which allow us to give new examples of multiplicity-free actions.