  Using the structure of the Boson-Fermion Fock space and an argument taken
from [2], we give a new proof of the triviality of the $L^2$ cohomology groups
on an abstract Wiener space, alternative to that given by Shigekawa [9]. We
apply some representation theory of the symmetric group to characterise the
spaces of exact and co-exact forms in their Boson-Fermion Fock space
representation.
