50.16 MinusCharacter

MinusCharacter( char, prime_powermap, prime )

Maps and Parametrized Maps) character chi^{p-} for the character chi = <char> and a prime p = <prime>, where chi^{p-} is defined by chi^{p-}(g) = ( chi(g)^p - chi(g^p) ) / p, and prime_powermap is the (possibly parametrized) p-th powermap.

    gap> t:= CharTable( "S7" );; pow:= InitPowermap( t, 2 );;
    gap> Congruences( t, t.irreducibles, pow, 2 );; pow;
    [ 1, 1, 3, 4, [ 2, 9, 10 ], 6, 3, 8, 1, 1, [ 2, 9, 10 ], 3, 4, 6,
      [ 7, 12 ] ]
    gap> chars:= Sublist( t.irreducibles, [ 2 .. 5 ] );;
    gap> List( chars, x-> MinusCharacter( x, pow, 2 ) );
    [ [ 0, 0, 0, 0, [ 0, 1 ], 0, 0, 0, 0, 0, [ 0, 1 ], 0, 0, 0, [ 0, 1 ] ],
      [ 15, -1, 3, 0, [ -2, -1, 0 ], 0, -1, 1, 5, -3, [ 0, 1, 2 ], -1, 0,
          0, [ 0, 1 ] ],
      [ 15, -1, 3, 0, [ -1, 0, 2 ], 0, -1, 1, 5, -3, [ 1, 2, 4 ], -1, 0,
          0, 1 ],
      [ 190, -2, 1, 1, [ 0, 2 ], 0, 1, 1, -10, -10, [ 0, 2 ], -1, -1, 0,
          [ -1, 0 ] ] ]

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