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In this paper, we study representations of a direct sum of Lie superalgebras. We deal with the question of whether the irreducible represen- tations of a finite direct sum of Lie superalgebras are obtained in case rep- resentations of each constituent are available. We give an affirmative answer to this question for finite weight representations of a class of Lie superalge- bras containing basic classical simple Lie superalgebras as well as affine Lie (super)algebras.
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