Abstract
We introduce super-analogues of the Schur functors defined by Akin, Buchsbaum and Weyman. These Schur superfunctors may be viewed as characteristic-free analogues of finite dimensional irreducible polynomial representations of the Lie superalgebra 𝔤𝔩(m|n) studied by Berele and Regev. Our construction realizes Schur superfunctors as objects of a certain category of strict polynomial superfunctors. We show that Schur superfunctors are indecomposable objects of this category. In characteristic zero, these correspond to the set of all simple supermodules for the Schur superalgebra, S(m|n, d), for any m, n, d ⩾ 0. We also provide decompositions of Schur bisuperfunctors in terms of tensor products of skew Schur superfunctors.
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Acknowledgments
The author wishes to thank Seok-Jin Kang and Myungho Kim for many helpful discussions and Jerzy Weyman for helpful correspondence. This paper was supported by the Sungkyun Research Fund, Sungkyunkwan University, 2016.
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Presented by Steffen Koenig.
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Axtell, J. On Schur Superfunctors. Algebr Represent Theor 21, 87–129 (2018). https://doi.org/10.1007/s10468-017-9705-0
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DOI: https://doi.org/10.1007/s10468-017-9705-0