## An explicit formula for the characters of the symmetric group

Page of Michel Lassalle

List of publications

Some preprints

Symmetric functions
and
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 :
[2]
2*p1
[3]
3*p2+3/2*n-3/2*n^2
means