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Instantons and affine algebras. I: The Hilbert scheme and vertex operators. (English) Zbl 0879.17011

From the abstract: “This is the first in a series of papers which describe the action of an affine Lie algebra with central charge \(n\) on the moduli space of \(U(n)\)-instantons on a four manifold \(X\). This generalizes work of H. Nakajima [Duke Math. J. 76, 365-416 (1995; Zbl 0826.17026)], who considered the case when \(X\) is an ALE space.”
“In the particular case of \(U(1)\)-instantons, which is essentially the subject of this present paper, the construction produces the basic representation after Frenkel-Kac”.

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
14C05 Parametrization (Chow and Hilbert schemes)
17B69 Vertex operators; vertex operator algebras and related structures

Citations:

Zbl 0826.17026
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