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

Comes, Jonathan; Wilson, Benjamin

doi:10.1090/S1088-4165-2012-00425-3

Deligne’s category $\underline {\operatorname {Re}}\!\operatorname {p}(GL_\delta )$ and representations of general linear supergroups
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by Jonathan Comes and Benjamin Wilson

Represent. Theory 16 (2012), 568-609

DOI: https://doi.org/10.1090/S1088-4165-2012-00425-3

Published electronically: December 3, 2012

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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 $\underline {\operatorname {Re}}\!\operatorname {p}(GL_\delta )$ and explain how to decompose their tensor products.

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