Jucys-Murphy elements and a presentation for partition algebras

Details Jucys-Murphy elements and a presentation for partition algebras Jucys-Murphy elements and a presentation for partition algebras

2010-09-10

arxiv.org/abs/1009.1939v3

Mathematics

Quantum Algebra

38 pages, 9 figures. Typos corrected and editorial changes made from v1 and v2

Scientific paper

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.

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