Obtaining the characters of the symmetric group corresponding to partitions in GAP

Question

Is there a way via the computer algebra system GAP to obtain the irreducible character of the symmetric group $S_n$ (over $\mathbb{C}$) corresponding to a given partition (via the canonical bijection)? So the input should be a partition and the output should be the corresponding character as a character in GAP (so that one can do things using existing GAP programs like calculating scalar products between characters or multiply two characters).

Answer 1

(This gets too long for comment.) You must use the generic (parameterized) character table for the "symmetric" group. And you must use CharacterParameters.

In your example:

gap> n:=4;;U:=Partitions(n);
[ [ 1, 1, 1, 1 ], [ 2, 1, 1 ], [ 2, 2 ], [ 3, 1 ], [ 4 ] ]
gap> tbl:=CharacterTable("symmetric",n);
CharacterTable( "Sym(4)" )
gap> irr:=Irr(tbl);;
gap> cp:=CharacterParameters(tbl);
[ [ 1, [ 1, 1, 1, 1 ] ], [ 1, [ 2, 1, 1 ] ], [ 1, [ 2, 2 ] ], [ 1, [ 3, 1 ] ],
  [ 1, [ 4 ] ] ]
gap> W:=[];;for i in [1..Length(U)] do
> pos:=PositionProperty(cp,x->x[2]=U[i]);
> Add(W,[U[i],irr[pos]]);
> od;
gap> W;
[ [ [ 1, 1, 1, 1 ], Character( CharacterTable( "Sym(4)",[ 1, -1, 1, 1, -1 ] ) ],
  [ [ 2, 1, 1 ], Character( CharacterTable( "Sym(4)" ), [ 3, -1, -1, 0, 1 ] )],
  [ [ 2, 2 ], Character( CharacterTable( "Sym(4)" ),[ 2, 0, 2, -1, 0 ] ) ],
  [ [ 3, 1 ], Character( CharacterTable( "Sym(4)" ), [ 3, 1, -1, 0, -1 ] ) ],
  [ [ 4 ], Character( CharacterTable( "Sym(4)" ), [ 1, 1, 1, 1, 1 ] ) ] ]