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J. Math. Phys. 36, 5979-6003 (1995)


Finite-dimensional representations of the quantum superalgebra u-q[gl(2/2)] .2. nontypical representations at generic-q

N. A. Ky, N. I. Stoilova

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 U-q[gl(2/2)]-modules W-q constructed in the previous paper are either irreducible or indecomposable. If a module W-q is indecomposable, i.e., when the condition (4.41) in the previous paper does not hold, there exists an invariant maximal submodule of W-q, say, I-k(q), such that the factor representation in the factor module W-q/I-k(q) is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra U-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. (C) 1995 American Institute of Physics.