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The center of the partition algebra

Creedon, S. (2021). The center of the partition algebra. Journal of Algebra, 570, pp. 215-266. doi: 10.1016/j.jalgebra.2020.10.041


In this paper we show that the center of the partition algebra , in the semisimple case, is given by the subalgebra of supersymmetric polynomials in the normalised Jucys-Murphy elements. For the non-semisimple case, such a subalgebra is shown to be central, and in particular it is large enough to recognise the block structure of . This allows one to give an alternative description for when two simple -modules belong to the same block.

Publication Type: Article
Publisher Keywords: Partition algebra; Center; Representation theory; Jucys-Murphy elements; Supersymmetric polynomials
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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