Let $\mathcal{B}$ be the flag variety and $\mathcal{N} \subset \mathfrak{g}$ is the nilpotent cone. We know that the Springer resolution$$\mu: T^*\mathcal{B}\rightarrow \mathcal{N}$$
is the moment map, if we identify $\mathfrak{g}$ with $\mathfrak{g}^* $ by the Killing form and consider $\mathcal{N} \subset \mathfrak{g}$ as a subset of $\mathfrak{g}^*$.
As far as I know, the geometric construction of Weyl group and $U(sl_n)$ does not involve moment map or even symplectic geometry, as in the paper "Geometric Methods in Representation Theory of Hecke Algebras and Quantum Groups"
My question is: what is the consequence of the fact that the Springer resolution is a moment map?
