JucysMurphy elements and a presentation for partition algebras
We give a new presentation for the partition algebras. This presentation was discovered in the course of establishing an inductive formula for the partition algebra JucysMurphy elements defined by Halverson and Ram (Eur. J. Comb. 26:869921, 2005). Using SchurWeyl duality we show that our recursive formula and the original definition of JucysMurphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra JucysMurphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.
jucysmurphy elements presentation partition algebras central elements