Deligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups

Abstract

We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric Schur polynomials, and give a method for decomposing their tensor products. Along the way, we describe indecomposable objects in Re _ p ⁡ ( G L δ ) \underline {\operatorname {Re}}\!\operatorname {p}(GL_\delta ) and explain how to decompose their tensor products.