Symmetric functions and Jucys-Murphy elements

  Page of Michel Lassalle
  List of publications
  Some preprints
  Tables for
characters of the
symmetric group

  Tables for
Jack polynomials :

  Jack polynomials
and alpha-contents

  A conjecture for
Jack polynomials

  Jack polynomials
and free cumulants
  This page gives new data for the class expansion of the Hall-Littlewood polynomial taken at the Jucys-Murphy elements of the symmetric group. Our results have been published there.

  We consider the Hall-Littlewood polynomial Pk(x1,x2,...,xn;z), its specialization at the Jucys-Murphy elements J1,J2,...,Jn of the symmetric group of n letters, and the development of this specialization in terms of the Farahat-Higman classes, i.e. we write

  We give the generating functions of the coefficients, i.e.

  For z = 0 ( respectively z = 1 ), our tables correspond to the case of complete symmetric functions hk (respectively power sums pk).


  Tables giving the function &Phi&rho(t) for weight of &rho from 3 to 14

  Tables for bigger values may be given upon request.

  Our results are in Maple format. They should be read as follows.

  • The letter z stands for the parameter of the Hall-Littlewood polynomial.
  • The letter q stands for exp(t).
  • The table gives first the partition &rho, then &Phi&rho(t).

Example :


Last modified : May 8, 2010

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