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, i.e.
  
  
• &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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