Finite-dimensional representations of the quantum superalgebra U(sub q)(gl(2/2)) II: Nontypical representations at generic q

摘要

The construction approach proposed in the previous paper Ref.1 allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra U(sub q)(gl(2/2)). The finite-dimensional U(sub q)(gl(2/2))-modules W(sup q) constructed in Ref.1 are either irreducible or indecomposable. If a module W(sup q) is indecomposable, i.e. when the condition (4.41) in Ref.1 does not hold, there exists an invariant maximal submodule of W(sup q), to say I(sup q)(sub k), such that the factor-representation in the factor-module W(sup q)/I(sup q)(sub k) is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra U(sub q)(gl(2/2)) are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly. (author). 23 refs. (Atomindex citation 26:038536)