Quiver varieties and Frenkel-Kac construction

Details Quiver varieties and Frenkel-Kac construction Quiver varieties and Frenkel-Kac construction

2007-03-04

arxiv.org/abs/math/0703107v1

J. Algebra 321 (2009), no. 12, 3764--3789

Mathematics

Representation Theory

28pages

Scientific paper

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 $A$ the former is obtained by Frenkel-Kac construction from the
latter.

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