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Representation Theory

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Spin polynomial functors and representations of Schur superalgebras

Author: Jonathan Axtell
Journal: Represent. Theory 17 (2013), 584-609
MSC (2010): Primary 16D90, 17A70, 18D20, 20G05, 20G43; Secondary 14L15
Published electronically: December 6, 2013
MathSciNet review: 3138585
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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\vert 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\vert 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

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.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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