An explicit formula for
the characters of the symmetric group

  Page of Michel Lassalle
  List of publications
  Some preprints
  Symmetric functions
Jucys-Murphy elements

  Tables for
Jack polynomials :

  Jack polynomials
and alpha-contents

  A conjecture for
Jack polynomials

  Jack polynomials
and free cumulants
  This page gives some data for the normalized characters of the symmetric group.
  Our results have been obtained by using a new formula expliciting these characters.
  This explicit formula has been announced here and published there.
  We consider the symmetric group of n letters, an irreducible representation labelled by a partition &lambda and a class of permutations labelled by a partition (&mu, 1, ..., 1).

  Our formula gives the normalized character

in terms of the "contents" of the partition &lambda.


  Here we list these characters for any partition &mu with no part 1, such that weight(&mu) - length(&mu) < 15.
  Tables giving the normalized characters for weight(&mu) - length(&mu)  Tables for bigger values may be given upon request.

  Our results are in Maple format. They should be read as follows.
  • The partition &lambda is kept arbitrary.
    The letter p_k (k > 0) stands for the k-th power sum of the contents of &lambda, i.e.

  • &mu denotes a partition without any part 1.
  • Each table gives first the partition &mu, then
Example :

Last modified : July 18, 2009

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