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

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.Comment: Latex file, 49 page

A Klein operator for paraparticles

It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of m parafermions and a set of n parabosons. These two choices are known as “relative parafermion type” and “relative paraboson type”, and correspond to quite different underlying algebraic structures. In this short note we show how the two possibilities are related by a so-called Klein transformation