Vertex representations via finite groups and the McKay correspondence

Given a finite group Γ and a virtual character ξ on it, we construct a Fock space and associated vertex operators in terms of a representation ring of wreath products Γ ∼ Sn We recover the character tables of wreath products Γ ∼ Sn by vertex operator calculus. When Γ is a finite subgroup of SU2, is a finite subgroup of A D E type, which can be regarded as a new form of McKay correspondence.