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Defining an affine partition algebra

De Visscher, M. ORCID: 0000-0003-0617-2818 & Creedon, S. (2023). Defining an affine partition algebra. Algebras and Representation Theory, 26(6), pp. 2913-2965. doi: 10.1007/s10468-022-10196-5


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.

Publication Type: Article
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Publisher Keywords: affine partition algebra, Schur-Weyl duality, Heisenberg category
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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