  Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-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 $\Gamma$. 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.
