

An explicit formula for
the characters of the symmetric group

Page of Michel Lassalle
List of publications
Some preprints
Symmetric functions and JucysMurphy elements
Tables for Jack polynomials :
Jack polynomials and alphacontents
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 kth 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*n3/2*n^2
means



Last modified : July 18, 2009
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