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Article overview
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Hilbert schemes and W algebras | Wei-Ping Li
; Zhenbo Qin
; Weiqiang Wang
; | Date: |
5 Nov 2001 | Journal: | Intern. Math. Res. Notices 27 (2002) 1427--1456. | Subject: | Algebraic Geometry; Quantum Algebra | math.AG hep-th math.QA | 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 $W_{1+infty}$-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 Heisenberg algebra generators. In addition, these Chern character operators are proved to be the zero-modes of vertex operators. | Source: | arXiv, math.AG/0111047 | Services: | Forum | Review | PDF | Favorites |
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