Twisted Vertex Representations via Spin Groups and the Mckay Correspondence

We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ and a virtual character of Γ we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products Γ ≀ S̃n of Γ and a double cover of the symmetric group Sn for all n. When Γ is a subgroup of SL2(C) with the McKay virtual character, our construction gives a group theoretic realization of the basic representations of the twisted affine and twisted toroidal algebras. When Γ is an arbitrary finite group and the virtual character is trivial, our vertex operator construction yields the spin character tables for Γ ≀ S̃n.