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arXiv · 2005.00600

The Center of the Partition Algebra

Samuel Creedon
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Abstract

In this paper we show that the center of the partition algebra $\mathcal{A}_{2k}(\delta)$, 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 $\mathcal{A}_{2k}(\delta)$. This allows one to give an alternative description for when two simple $\mathcal{A}_{2k}(\delta)$-modules belong to the same block.

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BibTeXRIS

Samuel Creedon. 2020-05-01. The Center of the Partition Algebra. https://doi.org/10.1016/j.jalgebra.2020.10.041

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