Hilbert schemes and W algebras

2001/11/30 by Wei-Ping Li, Zhenbo Qin, Weiqiang Wang
Mathematics · Physics and Astronomy · #math.AG #hep-th #math.QA

paper · pdf

published as Intern. Math. Res. Notices 27 (2002) 1427--1456. · 26 pages, latex, mild changes, to appear in IMRN

arxiv created 2002/02/26 · arxiv updated 2009/11/30

Abstract

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+∞-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 Heisenberg algebra generators. In addition, these Chern character operators are proved to be the zero-modes of vertex operators.

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