Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. II. Nontypical representations at generic q

Abstract

The construction approach proposed in the previous paper [N. A. Ky, J. Math. Phys. 35, 2583 (1994)] allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)]. The finite-dimensional Uq[gl(2/2)]-modules Wq constructed in the previous paper are either irreducible or indecomposable. If a module Wq is indecomposable, i.e., when the condition (4.41) in the previous paper does not hold, there exists an invariant maximal submodule of Wq, say, Iqk, such that the factor representation in the factor module Wq/Iqk is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra Uq[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.