51.12 Powermap

Powermap( tbl, prime )
Powermap( tbl, prime, parameters )

returns a list of possibilities for the prime-th powermap of the character table tbl.

The optional record parameters may have the following fields:

chars:

a list of characters which are used for the check of kernels (see ConsiderKernels), the test of congruences (see Congruences) and the test of scalar products of symmetrisations (see PowermapsAllowedBySymmetrisations); the default is tbl.irreducibles

powermap:

a (parametrized) map which is an approximation of the desired map

decompose:

a boolean; if true, the symmetrisations of chars must have all constituents in chars, that will be used in the algorithm; if chars is not bound and tbl.irreducibles is complete, the default value of decompose is true, otherwise false

quick:

a boolean; if true, the subroutines are called with the option "quick"; especially, a unique map will be returned immediately without checking all symmetrisations; the default value is false

parameters:

a record with fields maxamb, minamb and maxlen which control the subroutine PowermapsAllowedBySymmetrisations: It only uses characters with actual indeterminateness up to maxamb, tests decomposability only for characters with actual indeterminateness at least minamb and admits a branch only according to a character if there is one with at most maxlen possible minus-characters.

    # cf.\ example in "InitPowermap"
    gap> t:= CharTable( "U4(3).4" );;
    gap> pow:= Powermap( t, 2 );
    [ [ 1, 1, 3, 4, 5, 2, 2, 8, 3, 4, 11, 12, 6, 14, 9, 1, 1, 2, 2, 3, 4,
          5, 6, 8, 9, 9, 10, 11, 12, 16, 16, 16, 16, 17, 17, 18, 18, 18,
          18, 20, 20, 20, 20, 22, 22, 24, 24, 25, 26, 28, 28, 29, 29 ] ]

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