  The $GL(1|1)$ WZW model in the free field realization that uses the $bc$
system is revisited. By bosonizing the $bc$ system we describe the
Neveu--Schwarz and Ramond sector modules $\mathcal
V^{\text{NS}}_{en}=\bigoplus_{l\in\mathbb Z}\mathcal V^l_{en}$ and $\mathcal
V^{\text{R}}_{en}=\bigoplus_{l\in\mathbb Z+{1\over2}}\mathcal V^l_{en}$ in
terms of the subspaces of a given fermion number $l$. We show that there are
two sectors of mutually local operators, each consists of all Neveu--Schwarz
operators and of Ramond operators with either integer or half-integer spins.
Conformal blocks and structure constants are found for operators that
correspond the highest weight vectors of the spaces $\mathcal V^l_{en}$. The
crossing and braiding matrices are considered and the hexagon and pentagon
equations are shown to be satisfied for typical modules. The degenerate case of
conformal blocks with atypical (logarithmic) modules as intermediate states is
considered. The known conformal block decomposition of correlation functions in
the degenerate case is shown to be related to the degeneration splitting in the
crossing and braiding relations. The scalar product in atypical modules is
discussed. The decomposition of unity in the full correlation functions in the
degenerate case in terms of this scalar product is explained.
