Abstract
We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space and mixed tensor space, respectively, over the group algebra of the symmetric group and the Brauer wall algebra, respectively. Our main new results are the second part of the mixed Schur-Weyl dualities and mixed super Schur-Weyl dualities over an infinite ground field of positive characteristic.
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Acknowledgements
The author would like to thank the anonymous referee for the suggestions that greatly improved the presentation. Also, the author thanks Friederike Stoll for the conversation regarding the paper “Quantized mixed tensor space and Schur-Weyl duality.”
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Presented by: Milen Yakimov
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Marko, F. A Note on Schur-Weyl Dualities for GL(m) and GL(m|n). Algebr Represent Theor (2024). https://doi.org/10.1007/s10468-024-10290-w
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DOI: https://doi.org/10.1007/s10468-024-10290-w