Some results on Multiplicityfree spaces
Abstract
Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicityfree actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete classification of multiplicityfree 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 multiplicityfree actions on $M$ and multiplicityfree actions on the symplectic reduction and on the symplectic cut, which allow us to give new examples of multiplicityfree actions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402277
 Bibcode:
 2004math......2277B
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Representation Theory;
 primary 53C55. secondary 57S15
 EPrint:
 v1: 7 pages, added refernces and changed content v2: 22 may 2006, 12 pages, completely rewritten