Finite-Dimensional Representations of the Quantum Superalgebra U_q[gl(2/2)]: II. Nontypical representations at generic q release_2ozya6bqwzgiljuwuy3mv3u4fm

Abstract

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_q[gl(2/2)]. The finite--dimensional U_q[gl(2/2)]-modules W^q constructed in Ref. 1 are either irreducible or indecomposible. If a module W^q is indecomposible, i.e. when the condition (4.41) in Ref. 1 does not hold, there exists an invariant maximal submodule of W^q, to 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, indecomposible 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 analized and the matrix elements of all nontypical representations are written down explicitly.
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