# Tagged Questions

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### $TSU(n)$ completely integrable with 3 $SU(2)$ invariant functions?

Consider the Lie group $SU(n)$ endowed with the standard bi-invariant metric. Then $SU(n)$ can be viewed as a symmetric space of $K_{n,n} := SU(n) \times SU(n)$. Define $M := K_{n,n} /SU(n)$. Using ...
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### Origin of the name ''momentum map''

Why is the momentum map in the differential geometry of symmetries called the ''momentum'' (or ''moment'') map?
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### set of coisotropic orbits open and dense, iff group acts locally transitively almost everywhere

I worked now some time with coisotropic actions of Liegroups on manifolds. But there is one key fact, that I don't understand, although it is very central in my considerations. Let $(M,\omega)$ be a ...
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### Set of singular points for momentum map (with coisotropic action)

Let $G$ be a Lie-group acting on a connected symplectic manifold $M'$ in a hamiltonian way, with an $\operatorname{Ad}^*_G$-equivariant momentum map. Assuming $G$ acts properly on $M'$, we can ...
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### multiplicity free actions - Guillemin&Sternbergy collective integrability

In this post I already ask a similar question. Assume $M$ is a symplectic manifold of dimension $2n$. Assume $G$ is a Liegroup, $\mathfrak{g}$ be the Liealgebra and $\mathfrak{g^*}$ the corresponding ...
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### Polynomials pulled back by momentum maps

Let $G$ be a Lie group acting Hamiltonian on some real analytic symplectic manifold $(M, \omega)$, with an $G$-equivariant momentum map $\Phi \colon M \to \mathfrak{g}^*$. Assuming I can find ...