In the paper "New Quiver-Like varieties and Lie Superalgebras" by Rimanyi and Rozansky it is claimed that "There is a well-known correspondence between an $A_n$-type framed Nakajima quiver variety and a weight space in the tensor product of fundamental representations of $\mathfrak{gl}(N)$".
Where can I read about this correspondence, or if it is short enough to explain, can you give a sketch of how it works? I understand the geometry of the subclass of Nakajima quiver varieties as the cotangent bundles to flag varieties, and I can imagine how this might be related to representations of $\mathfrak{gl}(N)$, but I am not sure exactly how and I have no idea for general type $A$ quiver framings.