Mixed tensors of the general linear supergroup

We describe the image of the canonical tensor functor from Deligne's interpolating category Re_p(GLm−n) to Rep(GL(m|n)) attached to the standard representation. This implies explicit tensor product decompositions between any two projective modules and any two Kostant modules of GL(m|n), covering the decomposition between any two irreducible GL(m|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.