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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Spin polynomial functors and representations of Schur superalgebras
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by Jonathan Axtell PDF
Represent. Theory 17 (2013), 584-609 Request permission

Abstract:

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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Additional Information
  • Jonathan Axtell
  • Affiliation: Department of Mathematics, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea
  • Email: jdaxtell@snu.ac.kr
  • 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: https://doi.org/10.1090/S1088-4165-2013-00445-4
  • MathSciNet review: 3138585