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Geometric construction of representations of affine algebras

Hiraku Nakajima
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Abstract

Let $Γ$ be a finite subgroup of $\SL_2(\C)$. We consider $Γ$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the affine Lie algebra $\ag$ corresponding to $Γ$. If we replace homology groups by equivariant $K$-homology groups, we get a representation of the quantum toroidal algebra $\Ut$. We also discuss a higher rank generalization and character formulas in terms of intersection homology groups.

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Hiraku Nakajima. 2002-12-01. Geometric construction of representations of affine algebras. https://arxiv.org/abs/math/0212401

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