  Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we
construct a Fock space and associated vertex operators in terms of
representation ring of wreath products $\Gamma\sim S_n$. We recover the
character tables of wreath products $\Gamma\sim S_n$ by vertex operator
calculus. When $\Gamma$ is a finite subgroup of $SU_2$, our construction yields
a group theoretic realization of the basic representations of the affine and
toroidal Lie algebras of $ADE$ type, which can be regarded as a new form of
McKay correspondence.
