In this note we give an explicit geometric description of some of the Nakajima's quiver varieties. More precisely, we show that the Γ-equivariant Hilbert scheme X Γ[n] and the Hilbert scheme X[n] Γ (where X = C 2 , Γ ⊂ SL(C 2 ) is a finite subgroup, and X Γ is a minimal resolution of X/Γ) are quiver varieties for the affine Dynkin graph, corresponding to Γ via the McKay correspondence, the same dimension vectors, but different parameters ζ (for earlier results in this direction see [4,12,13]). In particular, it follows that the varieties X Γ[n] and X [n] Γ are diffeomorphic. Computing their cohomology (in the case Γ = Z/dZ) via the fixed points of (C * × C * )-action we deduce the following combinatorial identity: the number U CY (n, d) of uniformly coloured in d colours Young diagrams consisting of nd boxes coincides with the number CY (n, d) of collections of d Young diagrams with the total number of boxes equal to n. I was partially supported by RFFI grants 99-01-01144 and 99-01-01204.