Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. I. Typical representations

In a series of two papers all finite-dimensional irreducible representations and some indecomposible representations of the general linear Lie superalgebra gl(2/2) are constructed in a basis suitable for the decomposition gl(2/2)⊇gl(2)⊕gl(2). In this paper each induced gl(2/2) module W is represented as a direct sum of its irreducible gl(2)⊕gl(2) submodules Vi, 1≤i≤16. The basis Γ in W is chosen to consist of the union of all Γi, where Γi is an appropriate basis in each Vi. Expressions for the transformation of Γ under the action of the generators are written down for all induced and hence, also, for all typical gl(2/2) modules.