Hilbert schemes and W algebras

@article{Li2001HilbertSA,
  title={Hilbert schemes and W algebras},
  author={Wei-Ping Li and Zhenbo Qin and Weiqiang Wang},
  journal={arXiv: Algebraic Geometry},
  year={2001}
}
We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n. We compute explicitly the commutators among a set of linear basis elements of the W algebra, and identify this algebra with a $W_{1+\infty}$-type algebra. A precise formula of certain Chern character operators, which is essential for the construction of the W algebra, is established in terms of the… 

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