Deligne's category Rep(GL_δ) and representations of general linear supergroups

preprint2011arXivOpen access

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 Rep(GL_δ) and explain how to decompose their tensor products.

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