Paper detail

The Center of the Partition Algebra

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