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We classify indecomposable summands of mixed tensor powers of the naturalrepresentation for the general linear supergroup up to isomorphism. We alsogive a formula for the characters of these summands in terms of compositesupersymmetric Schur polynomials, and give a method for decomposing theirtensor products. Along the way, we describe indecomposable objects inRep(GL_\delta) and explain how to decompose their tensor products.

Deligne's category Rep(GL_\delta) and representations of general linear supergroups