Abstract

We give an explicit description of all inequivalent Heisenberg subalgebras of the affine Lie algebra\(g\hat l_n (\mathbb{C})\) and the associated vertex operator constructions of the level one integrable highest weight representations of this algebra. The construction uses multicomponent fermionic fields and yields a correspondence between bosons (elements of the Heisenberg subalgebra) and fermions.

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