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

Abstract

In the present paper we construct all typical finite-dimensional representations of the quantum Lie superalgebra $U_q[gl(2/2)]$ at generic deformation parameter $q$. As in the non-deformed case the finite-dimensional $U_q[gl(2/2)]$-module $W^q$ obtained is irreducible and can be decomposed into finite-dimensional irreducible $U_q[gl(2)\oplus gl(2)]$-submodules $V_k^q$

published version. Some formulae are rewritten in more compact form

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