An explicit formula for
the characters of the symmetric group

  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)

• from 1 to 12 (included)
  (0.5 Mo)
• from 13 to 14 (included)
  (1.55 Mo)

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

Example :
[2]
2*p1
[3]
3*p2+3/2*n-3/2*n^2
means

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