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Explicit expressions for the generators of the quantum superalgebra$U_q[gl(n/m)]$ acting on a class of irreducible representations are given. Theclass under consideration consists of all essentially typical representations:for these a Gel'fand-Zetlin basis is known. The verification of the quantumsuperalgebra relations to be satisfied is shown to reduce to a set of$q$-number identities.Comment: 12 page

Finite-dimensional representations of the quantum superalgebraU q[gl(n/m)] and relatedq-identities