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Explicit representations of super-Kac-Moody algebra are constructed in terms of 2d-free fermions which form a non-linear representation of supersymmetry with the fermions grouped with the generators of the algebra into superfields. It is shown how the most general construction of this type corresponds to homogeneous spacesG/H and how supersymmetry alone is responsible for that structure.

Super-Kac-Moody algebras and supersymmetric 2d-free fermions