Dear Mrs. and Mr. Forum,

Steve Fisk asked for a function that returns or prints information
about eigenvalues of representations of symmetric groups.

If one constructs the character table of the symmetric group S_n using
't:= CharTable( "Symmetric", n )' then 't' contains the partitions
that parametrize the conjugacy classes and the irreducible characters.

The partition corresponding to the 'j'-th conjugacy class is
't.classparam[j][2]', the partition corresponding to the 'i'-th
irreducible character is 't.irredinfo[i].charparam[2]'.

So a function that prints the two partitions and the eigenvalues
of the 'i'-th character at class 'j' may look like this.

Fisk := function( t, i, j )
    Print( t.irredinfo[i].charparam[2], " ",
           t.classparam[j][2], " ",
           Eigenvalues( t, t.irreducibles[i], j ), "\n" );
    end;

Kind regards
Thomas Breuer
(sam@math.rwth-aachen.de)