## Spin polynomial functors and representations of Schur superalgebras

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- by Jonathan Axtell
- Represent. Theory
**17**(2013), 584-609 - DOI: https://doi.org/10.1090/S1088-4165-2013-00445-4
- Published electronically: December 6, 2013
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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 $GL(m|n)$ 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 $\mathsf {Pol}^{\mathrm {II}}_{d,\Bbbk }$.## References

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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: 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