(sl)over-cap(2|1) and (D)over-cap (2|1;α) as vertex operator extensions of dual affine sl(2) algebras

We discover a realisation of the affine Lie superalgebra (sl) over cap (2/1) and of the exceptional affine super-algebra (D) over cap (2/1; alpha) as vertex operator extensions of two (sl) over cap (2) algebras with "dual" levels land an auxiliary level-1 (sl) over cap (2) algebra. The duality relation between the levels is (k(1) + 1)(k(2) + 1) = 1. We construct the representation of (sl) over cap (2/1l)(k1) on a sum of tensor products of (sl) over cap (2)(k1), (sl) over cap (2)(k2), and (sl) over cap (2)(1) modules and decompose it into a direct sum over the (sl) over cap (2/1)(k1), spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to (D) over cap (2/1; (k)2)(k1) is traced to the properties of (sl) over cap (2) + (sl) over cap (2) + (sl) over cap (2) embeddings into (D) over cap (2/1; alpha) and their relation with the dual (sl) over cap (2) pairs. Conversely, we show how the (sl) over cap (2)(k2) representations are constructed from (sl) over cap (2/1)(k1) representations.