In [1], Maffei proved a certain relationship between quiver varieties of type A and the geometry of partial ag varieties over the nilpotent cone. This relation was conjectured by Nakajima, and Nakajima proved his conjecture for a simple case. In the Maffei`s proof, the key step was a reduction of the general case of the conjecture to the simple case treated by Nakajima through a certain isomorphism. In this paper, we study properties of this isomorphism.