Primary fields and screening currents of gl(2|2) non-unitary conformal field theory

The non-semisimple $gl(2\mathrm{\mid }2{)}_k$ current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of $gl(2\mathrm{\mid }2)$ and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.