The operator spaces $H_n^k$ $1\le k\le n$, generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of $C^*$-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. As an application, the completely bounded Banach-Mazur distance from $H_n^k$ to row or column space is explicitly calculated. This is joint work with Matt Neal.
An overview of "operator space theory" will be given.