50.25 Power

Power( powermap, chars, n )

returns the list of indirections of the characters chars by the n-th powermap; for a character chi in chars, this indirection is often called chi^{(n)}. The powermap is calculated from the (necessarily stored) powermaps of the prime divisors of n if it is not stored in powermap (see Powmap).

Note that chi^{(n)} is in general only a virtual characters.

    gap> t:= CharTable( "A5" );; Power( t.powermap, t.irreducibles, 2 );
    [ [ 1, 1, 1, 1, 1 ], [ 3, 3, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ],
      [ 3, 3, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ], [ 4, 4, 1, -1, -1 ],
      [ 5, 5, -1, 0, 0 ] ]
    gap> MatScalarProducts( t, t.irreducibles, last );
    [ [ 1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 1 ], [ 1, 0, -1, 0, 1 ],
      [ 1, -1, -1, 1, 1 ], [ 1, -1, -1, 0, 2 ] ]

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