Jucys–Murphy elements and a presentation for partition algebras

@article{Enyang2013JucysMurphyEA,
  title={Jucys–Murphy elements and a presentation for partition algebras},
  author={John Enyang},
  journal={Journal of Algebraic Combinatorics},
  year={2013},
  volume={37},
  pages={401-454}
}
  • John Enyang
  • Published 2013
  • Mathematics
  • Journal of Algebraic Combinatorics
  • 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… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    References

    Publications referenced by this paper.
    SHOWING 1-7 OF 7 REFERENCES

    Okounkov, A new approach to representation theory of symmetric groups II

    • A. A. Vershik
    • J. Math. Sci. (N. Y.)
    • 2005

    in: Subfactors: Proceedings of the Taniguchi Symposium on Operator Algebras (Kuzeso

    • V.F.R Jones, The Potts model, the symmetric group
    • 1993), River Edge, NJ, World Sci. Publishing,
    • 1994
    VIEW 2 EXCERPTS

    MR 1103994 ( 92 m : 82030 ) [ Mar 1 ] P . Martin , Temperley - Lieb algebras for nonplanar statistical mechanics – the partition algebra construction

    • NJ Teaneck
    • J . Knot Theory Ramifications
    • 1991

    vol

    • P. Martin, Potts models, related problems in statistical mechanics, Series on Advances in Statistical Mechanics
    • 5, World Scientific Publishing Co. Inc., Teaneck NJ,
    • 1991
    VIEW 1 EXCERPT