Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

We prove that the tensor product of a simple and a finite dimensional sln-module has finite type socle. This is applied to reduce classification of simple q(n)-supermodules to that of simple sln-modules. Rough structure of simple q(n)-supermodules, considered as sln-modules, is described in terms of the combinatorics of category O.