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Representation Theory

ISSN 1088-4165



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

Authors: Jonathan Comes and Benjamin Wilson
Journal: Represent. Theory 16 (2012), 568-609
MSC (2010): Primary 17B10, 18D10
Published electronically: December 3, 2012
MathSciNet review: 2998810
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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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Additional Information

Jonathan Comes
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Benjamin Wilson
Affiliation: Dieffenbachstraße 27, 10967 Berlin, Germany

Received by editor(s): September 5, 2011
Received by editor(s) in revised form: July 31, 2012
Published electronically: December 3, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.