68.2 Basic Operations for Class Functions

For a class function psi of the group G, say, the character table of G is stored as value of UnderlyingCharacterTable. The ordering of entries in the list psi (see ValuesOfClassFunction) refers to the ordering of conjugacy classes in this character table.

If psi is an ordinary class function then the underlying character table is the ordinary character table of G (see OrdinaryCharacterTable), if psi is a class function in characteristic p ¹ 0 then the underlying character table is the p-modular Brauer table of G (see BrauerTable). So the underlying characteristic of psi can be read off from the underlying character table.

is the list of values of the class function psi, the i-th entry being the value on the i-th conjugacy class of the underlying character table (see UnderlyingCharacterTable).

gap> g:= SymmetricGroup( 4 );
Sym( [ 1 .. 4 ] )
gap> psi:= TrivialCharacter( g );
Character( CharacterTable( Sym( [ 1 .. 4 ] ) ), [ 1, 1, 1, 1, 1 ] )
gap> UnderlyingCharacterTable( psi );
CharacterTable( Sym( [ 1 .. 4 ] ) )
gap> ValuesOfClassFunction( psi );
[ 1, 1, 1, 1, 1 ]
gap> IsList( psi );
true
gap> psi[1];
1
gap> Length( psi );
5
gap> IsBound( psi[6] );
false
gap> Concatenation( psi, [ 2, 3 ] );
[ 1, 1, 1, 1, 1, 2, 3 ]

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