Quantum Vertex Representations via Finite Groups and the Mckay Correspondence
نویسندگان
چکیده
We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in terms of wreath products of Γ×C and the symmetric groups. An important special case is obtained when Γ is a finite subgroup of SU2, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of ADE type.
منابع مشابه
Two-parameter quantum vertex representations via finite groups and the McKay correspondence
We introduce two-parameter quantum toroidal algebras of simply laced types and provide their group theoretic realization using finite subgroups of SL2(C) via McKay correspondence. In particular our construction contains a realization of the vertex representation of the two-parameter quantum affine algebras of ADE types.
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