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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Spin polynomial functors and representations of Schur superalgebras
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by Jonathan Axtell
Represent. Theory 17 (2013), 584-609
Published electronically: December 6, 2013


We introduce categories of homogeneous strict polynomial functors, $\mathsf {Pol}^{\mathrm {I}}_{d,\Bbbk }$ and $\mathsf {Pol}^{\mathrm {II}}_{d,\Bbbk }$, defined on vector superspaces over a field $\Bbbk$ of characteristic not equal 2. These categories are related to polynomial representations of the supergroups $GL(m|n)$ and $Q(n)$. In particular, we prove an equivalence between $\mathsf {Pol}^{\mathrm {I}}_{d,\Bbbk }$, $\mathsf {Pol}^{\mathrm {II}}_{d,\Bbbk }$ and the category of finite dimensional supermodules over the Schur superalgebra $\mathcal {S}(m|n,d)$, $\mathcal {Q}(n,d)$ respectively provided $m,n \ge d$. We also discuss some aspects of Sergeev duality from the viewpoint of the category $\mathsf {Pol}^{\mathrm {II}}_{d,\Bbbk }$.
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Bibliographic Information
  • Jonathan Axtell
  • Affiliation: Department of Mathematics, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea
  • Email:
  • Received by editor(s): February 8, 2013
  • Received by editor(s) in revised form: May 28, 2013
  • Published electronically: December 6, 2013
  • Additional Notes: This work was supported by the BRL research fund grant #2013055408 of the National Research Foundation of Korea.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 584-609
  • MSC (2010): Primary 16D90, 17A70, 18D20, 20G05, 20G43; Secondary 14L15
  • DOI:
  • MathSciNet review: 3138585