Representations of the non-semisimple superalgebra gls2u2d in the standard basisare investigated by means of the vector coherent state method and boson-fermionrealization. All finite-dimensional irreducible typical and atypical representationsand lowest weight (indecomposable) Kac modules of gls2u2d are constructed explicitlythrough the explicit construction of all gls2d % gls2d 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 ofgls2u2d in explicit form, essential for the construction of primary fields of thecorresponding current superalgebra at arbitrary level

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