Quiver varieties and Frenkel-Kac construction

preprint2007arXivOpen access

Abstract

An affine Lie algebra acts on cohomology groups of quiver varieties of affine type. A Heisenberg algebra acts on cohomology groups of Hilbert schemes of points on a minimal resolution of a Kleinian singularity. We show that in the case of type AA the former is obtained by Frenkel-Kac construction from the latter.

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