Mixed tensors of the general linear supergroup

We describe the image of the canonical tensor functor from Deligne's interpolating category Rep(GL(m-n)) to Rep(GL(mln)) attached to the standard representation. This implies explicit tensor product decompositions between any two projective modules and any two Kostant modules of GL(m vertical bar n), covering the decomposition between any two irreducible GL(m vertical bar 1)-representations. We also obtain character and dimension formulas. For m > n we classify the mixed tensors with non -vanishing superdimension. For m = n we characterize the maximally atypical mixed tensors and show some applications regarding tensor products. (C) 2017 Elsevier Inc. All rights reserved.