Abstract
We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl duality between the symmetric group and the partition algebra. We also relate it to the affine partition category recently defined by J. Brundan and M. Vargas. Moreover, we show that this affine partition category is a full monoidal subcategory of the Heisenberg category.
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Samuel Creedon conducted this work while holding a PhD studentship at City, University of London, funded by EPSRC. The authors have no competing interests to declare that are relevant to the content of this article.
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Presented by: Andrew Mathas
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Creedon, S., De Visscher, M. Defining an Affine Partition Algebra. Algebr Represent Theor 26, 2913–2965 (2023). https://doi.org/10.1007/s10468-022-10196-5
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DOI: https://doi.org/10.1007/s10468-022-10196-5