Heisenberg algebra and Hilbert schemes of points on projective surfaces

  title={Heisenberg algebra and Hilbert schemes of points on projective surfaces},
  author={Hiraku Nakajima},
  journal={Annals of Mathematics},
  • H. Nakajima
  • Published 20 July 1995
  • Mathematics
  • Annals of Mathematics
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… 


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