Some Results on Multiplcity-free Spaces
نویسندگان
چکیده
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 −→ 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 onM and multiplicity-free actions on the symplectic reduction and on the symplectic cut, which allow us to give new examples of multiplicity-free actions.
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