# Heisenberg algebra and Hilbert schemes of points on projective surfaces

@article{Nakajima1995HeisenbergAA, title={Heisenberg algebra and Hilbert schemes of points on projective surfaces}, author={Hiraku Nakajima}, journal={Annals of Mathematics}, year={1995}, volume={145}, pages={379-388} }

The purpose of this paper is to throw a bridge between two seemingly unrelated subjects. One is the Hilbert scheme of points on projective surfaces, which has been intensively studied by various people (see e.g. [I], [Br], [ES], [G61], [G62]). The other is the infinite dimensional Heisenberg algebra which is closely related to affine Lie algebras (see e.g. [K]). We shall construct a representation of the Heisenberg algebra on the homology group of the Hilbert scheme. In other words, the…

## 332 Citations

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