Tensor product representations

Abstract

In this paper, we study representations of a direct sum of Lie superalgebras. We deal with the question of whether the irreducible representations of a finite direct sum of Lie superalgebras are obtained in case representations of each constituent are available. We give an affirmative answer to this question for finite weight representations of a class of Lie superalgebras containing basic classical simple Lie superalgebras as well as affine Lie (super)algebras. © 2022 Elsevier Inc.