The operator spaces
H
n
k
H_n^k
,
1
≤
k
≤
n
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
∗
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. The completely bounded Banach-Mazur distance from
H
n
k
H_n^k
to a row or column space is explicitly calculated.