GAP Manual: 50.2. MatScalarProducts

MatScalarProducts( tbl, chars1, chars2 )
MatScalarProducts( tbl, chars )

For a character table tbl and two lists chars1, chars2 of characters, the first version returns the matrix of scalar products (see ScalarProduct); we have

MatScalarProducts( tbl, chars1, chars2 )[i][j] = ScalarProduct( tbl, chars1[j], chars2[i] ),

i.e., row i contains the scalar products of chars2[i] with all characters in chars1.

The second form returns a lower triangular matrix of scalar products:

MatScalarProducts( tbl, chars )[i][j] = ScalarProduct( tbl, chars[j], chars[i] )

for j leqi.

    gap> t:= CharTable( "A5" );;
    gap> chars:= Sublist( t.irreducibles, [ 2 .. 4 ] );;
    gap> chars:= Set( Tensored( chars, chars ) );;
    gap> MatScalarProducts( t, chars );
    [ [ 2 ], [ 1, 3 ], [ 1, 2, 3 ], [ 2, 2, 1, 3 ], [ 2, 1, 2, 2, 3 ],
      [ 2, 3, 3, 3, 3, 5 ] ]