Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: II. Nontypical representations at generic $q$

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.

Latex file, 49 pages

References in corpus (2)

• Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities
• Finite-Dimensional Representations of the Quantum Superalgebra U${}_q$[gl(2/2)]: I. Typical representations at generic $q$

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