Bosonic and fermionic realizations of the affine algebra gl(n)

Abstract

We give an explicit description of all inequivalent Heisenberg subalgebras of the affine Lie algebra gl(n) and the associated vertex operator constructions of the level one integrable highest weight representations of this algebra. The construction uses multicomponent fermionicfields and yields a correspondence between bosons (elements of the Heisenbergsubalgebra) and fermions.