Event description
Abstract: In this talk we discuss a reduction principle in the particular case of coisotropic actions. These actions were introduced by Guillemin and Sternberg in '84 as a symplectic analogue of multiplicity-free unitary representations of Lie groups in Hilbert spaces.
By definition, a coisotropic action is a symplectic action whose orbits in an open and dense subset are coisotropic submanifolds.
We first prove that a proper action is coisotropic if and only if it is multiplicity-free, i.e. the Lie subalgebra of invariant functions is Abelian.
We then show that a reduction principle holds for coisotropic actions. By this we mean that an action is coisotropic if and only if the subaction by a closed subgroup on the core relative to a principal isotropy is coisotropic.
This is a joint work with Prof. Leonardo Biliotti and Victor Gustavo May Custodio.