Abstract

We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A₁ using vertex operators based on bosonic fields. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k₀,k₁) with k₀≠0. 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 afine Lie algebra sl₂.

Keywords

toroidal Lie algebra, vertex operator, bosonic realization

Mathematical Subject Classification

Primary: 17B65, 17B69

Authors