51.13 SubgroupFusions

SubgroupFusions( subtbl, tbl )
SubgroupFusions( subtbl, tbl, parameters )

returns the list of all subgroup fusion maps from subtbl into tbl.

The optional record parameters may have the following fields:

chars:

a list of characters of tbl which will be restricted to subtbl, (see FusionsAllowedByRestrictions); the default is tbl.irreducibles

subchars:

a list of characters of subtbl which are constituents of the retrictions of chars, the default is subtbl.irreducibles

fusionmap:

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

decompose:

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

permchar:

a permutation character; only those fusions are computed which afford that permutation character (see CheckPermChar)

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 FusionsAllowedByRestrictions: 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 restrictions.

    # cf.\ example in "FusionsAllowedByRestrictions"
    gap> s:= CharTable( "U3(3)" );; t:= CharTable( "J4" );;
    gap> SubgroupFusions( s, t, rec( quick:= true ) );
    [ [ 1, 2, 4, 4, 5, 5, 6, 10, 12, 13, 14, 14, 21, 21 ],
      [ 1, 2, 4, 4, 5, 5, 6, 10, 13, 12, 14, 14, 21, 21 ],
      [ 1, 2, 4, 4, 6, 6, 6, 10, 12, 13, 15, 15, 22, 22 ],
      [ 1, 2, 4, 4, 6, 6, 6, 10, 12, 13, 16, 16, 22, 22 ],
      [ 1, 2, 4, 4, 6, 6, 6, 10, 13, 12, 15, 15, 22, 22 ],
      [ 1, 2, 4, 4, 6, 6, 6, 10, 13, 12, 16, 16, 22, 22 ] ]

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