Let $G=GL_n(\mathbb{C})$ and $X_{\omega}=\overline{B_-wB/B}\subset G/B$ be a Schubert variety. Denote by $C(X_\omega)$ the conormal variety inside $T^*(G/B)$ , 
$\mu:T^*(G/B)\to \mathcal{N}$ the Springer resolution. 
It is known that $\mu(C(X_\omega))$ is a orbital variety inside $\mathcal{N}$. (orbital variety is defiend as a component of $(G\cdot x) \cap \mathfrak{u}$, $\mathfrak{u}$ is lower triangular matrix with zeros on digonal). $G$-orbits of $\mathcal{N}$ are indexed by partition of $n$.
Then we can get a map from ${Permutation}(n)\to Partition(n)$. Do we know anything about this map?