On tensor products of representations of Lie superalgebras

We consider typical finite dimensional complex irreducible representations of a basic classical simple Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for sl (m+1, n+1), osp (2, 2n), G (3) and F (4) under an additional assumption. This result is a Lie superalgebra analogue of Rajan's fundamental result MR2123935 on unique factorization of tensor products for finite dimensional complex simple Lie algebras.