General routinesCharacters of symmetric groupsBuilding or making such objectsEvaluation of characters

Evaluation of characters

The evaluation of the complete character table of the symmetric group with prescribed degree is done by A single character value is calculated by The class multiplication coefficients can be obtained as follows:
Example:
...
scan(PARTITION,a); println(a);
scan(PARTITION,b); println(b);
scan(PARTITION,c);  println(c);
c_ijk_sn(a,b,c,g); println(g);
...
The charactertable of the wreath product Sb wr Sa can be obtained by the following routine:
Example:
...
scan(INTEGER,a); scan(INTEGER,b);
kranztafel(a,b,c,d,e);
println(c); println(d); println(e);
...
Here is the routine for the central characters: A particular irreducible character is evaluated by There is a helpful coroutine which does the same but uses the character table which must have been computed before: Here is a routine that evaluates the character of Sn choose 2 induced by a given character of Sn via the natural embedding of Sn into the symmetric group Sn choose 2 on the set of pairs: For the decomposition of ordinary characters of symmetric groups into irreducible ones you can use
Example: The following program asks first for the degree of the symmetric group, then for the maximal and the minimal value of the character values of the symmetric group character. These values are initialised with random value inside the given limits. The class function is decomposed into irreducible characters.
...
{
OP a,b,c,d,e;
INT i;
anfang();
a=callocobject(); b=callocobject(); 
c=callocobject(); d=callocobject(); e=callocobject(); 
printeingabe("degree of S_n"); scan(INTEGER,a);
printeingabe("min value of character"); scan(INTEGER,c);
printeingabe("max value of character"); scan(INTEGER,d);
m_d_sc(a,b); println(b);
for (i=0L;i<S_SC_WLI(b);i++)
	random_integer(S_SC_WI(b,i),c,d);
println(b); reduce_symchar(b,e); println(e);
freeall(a); freeall(b); freeall(c); freeall(d); freeall(e);
ende();
}
...
This example uses a special case of the following routine: For the scalar product of characters there is the following routine at hand:
harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001

General routinesCharacters of symmetric groupsBuilding or making such objectsEvaluation of characters