  Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard
basis are investigated by means of the vector coherent state method and
boson-fermion realization. All finite-dimensional irreducible typical and
atypical representations and lowest weight (indecomposable) Kac modules of
$gl(2|2)$ are constructed explicitly through the explicit construction of all
$gl(2)\oplus gl(2)$ particle states (multiplets) in terms of boson and fermion
creation operators in the super-Fock space. This gives a unified and complete
treatment of finite-dimensional representations of $gl(2|2)$ in explicit form,
essential for the construction of primary fields of the corresponding current
superalgebra at arbitrary level.
