We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A1 using vertex operators based on bosonic elds. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k0;k1) with k00. We also construct a smaller module of level (k0;0) for the toroidal algebra from the Fock space using certain screening vertex operator, and this later representation generalizes the higher-level construction of the ane Lie algebra 2.
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