Jucys-Murphy elements and a presentation for partition algebras

Abstract

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 Jucys-Murphy elements defined by Halverson and Ram [European J. Combin. 26 (2005), 869-921]. Using Schur-Weyl duality we show that our recursive formula and the original definition of Jucys-Murphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra Jucys-Murphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.

39 pages, 9 figures. Typos corrected and editorial changes made from v1-3. The final publication is available at springerlink.com

References in corpus (1)

• A seminormal form for partition algebras

Cited by in corpus (6)

• A seminormal form for partition algebras
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• The Center of the Partition Algebra
• A new approach to the representation theory of the partition category
• Skew cell modules for diagram algebras
• On the modular representation theory of the partition algebra