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

  • Authors:

  • John Enyang

  • Affiliations:

  • Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia 3010 and School of Mathematics and Statistics F07, University of Sydney, Sydney, Australia 2006

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2013

  • Partition algebras

    European Journal of Combinatorics - Special issue on combinatorics and representation theory

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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 (Eur. J. Comb. 26:869---921, 2005). 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.