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.
Keywords
Cite
@article{arxiv.1009.1939,
title = {Jucys-Murphy elements and a presentation for partition algebras},
author = {John Enyang},
journal= {arXiv preprint arXiv:1009.1939},
year = {2012}
}
Comments
39 pages, 9 figures. Typos corrected and editorial changes made from v1-3. The final publication is available at springerlink.com