Let's consider a Hamiltonian action of a torus $T$ on a symplectic manifold $(M, \Omega)$. We denote by $\mu: M \rightarrow \mathfrak{t}^*$ the moment map and by $\Omega_\mathfrak{t}(X) := \Omega + <\mu, X>$ the associated equivariant symplectic form.
Let $dm_L:= \Omega^n/n!$ the Liouville measure on $M$ (with dim$M =2n$). We denote by $\mu_*(dm_L)$ the direct image of the measure $dm_L$.
I've come across the following equality:
$\mu_*(dm_L)=\frac{1}{i^n} \mathcal{F}(\int_M e^{i \Omega_\mathfrak{t}})$
I don't understand why does this equality hold, it's ambiguous for me, and couldn't find a reference which prove it!
Your help would be very appreciated!
