Characters of the Symmetric Group

Single Values

The method used to compute the value of a character on a permutation is the recursion formula of Murnaghan and Nakayama [James and Kerber, 1981, p. 60], except when computing the value of a character on the identity permutation a formula for the dimension of the representation indexed by a partition is used, [James and Kerber, 1981, p. 56].

SymmetricCharacterValue(pa, pe): SeqEnum, GrpPermElt -> RngElt

Computes the value of the irreducible character of the symmetric group of degree \(n\) indexed by the partition \(pa\) of weight \(n\) on the permutation \(pe\). When computing the value of the character on the identity permutation, i.e. the degree of the character, the dimension (hook) formula is used on the partition \(pa\).

Irreducible Characters

SymmetricCharacter(pa): SeqEnum -> AlgChtrElt

Return the character of the representation of the symmetric group of degree \(n\) indexed by the partition \(pa\) where \(pa\) has weight \(n\).

Character Table

SymmetricCharacterTable(d): RngIntElt -> SeqEnum

Return the character table of the symmetric group of degree \(d\).