A unified and complete construction of all finite dimensional irreducible representations of gl(2∣2)

Abstract

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)⊕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.