Representation of contractively complemented Hilbertian operator spaces on the Fock space

The operator spaces , , generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of -algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from to a row or column space is explicitly calculated.