51.29 Indirected

Indirected( char, paramap )

We have [ Indirected( char, paramap )[i] = char[ paramap[i] ], ] if this value is unique; otherwise it is set unknown (see chapter Unknowns). (For a parametrized indirection, see CompositionMaps.)

    gap> m12:= CharTable( "M12" );;
    gap> fus:= [ 1, 3, 4, [ 6, 7 ], 8, 10, [ 11, 12 ], [ 11, 12 ],
    >            [ 14, 15 ], [ 14, 15 ] ];;  # parametrized subgroup fusion
                                             # from $M_{11}$
    gap> chars:= Sublist( m12.irreducibles, [ 1 .. 6 ] );;
    gap> List( chars, x -> Indirected( x, fus ) );
    [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], 
      [ 11, 3, 2, Unknown(1), 1, 0, Unknown(2), Unknown(3), 0, 0 ], 
      [ 11, 3, 2, Unknown(4), 1, 0, Unknown(5), Unknown(6), 0, 0 ], 
      [ 16, 0, -2, 0, 1, 0, 0, 0, Unknown(7), Unknown(8) ], 
      [ 16, 0, -2, 0, 1, 0, 0, 0, Unknown(9), Unknown(10) ], 
      [ 45, -3, 0, 1, 0, 0, -1, -1, 1, 1 ] ]

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