The Center of the Partition Algebra

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.

33 pages

Cited by in corpus (1)

• A new approach to the representation theory of the partition category