It is easy to realize cotangent space to the flag variety $Fl=SL_n/B$ as a Nakajima quiver variety: consider the finite quiver of type A, the dimension vectors v=(1,2,...,n-1), w=(0,...,0,n); an appropriate stability condition (polarization) amounts to the condition that the arrow from the i-dimensional space to the (i+1)-dimensional one is injective, and we end up with a complete flag in the n-space, the arrows in the opposite direction giving a cotangent vector.

Now, if I understand correctly, the other stability conditions (of which there is n!) should produce quiver varieties which are also isomorphic to $T^*(Fl)$. How to see this, preferably using equally explicit linear algebra? Is it explained in the literature?