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We describe a well-known collection of vertex operators on the infinite wedgerepresentation as a limit of geometric correspondences on the equivariantcohomology groups of a finite-dimensional approximation of the Satograssmannian, by cutoffs in high and low degrees. We prove that locality, theboson-fermion correspondence, and intertwining relations with the Virasoroalgebra are limits of the localization expression for the composition of theseoperators. We then show that these operators are, almost by definition, theHilbert scheme vertex operators defined by Okounkov and the author in \cite{CO}when the surface is $\mathbb{C}^2$ with the torus action $z\cdot (x,y) =(zx,z^{-1}y)$.

Vertex Operators, Grassmannians, and Hilbert Schemes