Abstract

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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