GAP Manual: 48.45. GetFusionMap

GetFusionMap( source, destination )
GetFusionMap( source, destination, specification )

For character tables source and destination, GetFusionMap( source, destination ) returns the map field of the fusion stored on the character table source that has the identifier component destination.name;

GetFusionMap( source, destination, specification ) gets that fusion that additionally has the specification field specification.

Both versions adjust the ordering of classes of destination using destination.permutation (see SortClassesCharTable, Conventions for Character Tables). That is the reason why destination cannot be simply the identifier of the destination table.

If both source and destination are Brauer tables, GetFusionMap returns the fusion corresponding to that between the ordinary tables; for that, this fusion must be stored on source.ordinary.

If no appropriate fusion is found, false is returned.

    gap> s:= CharTable( "L2(11)" );;
    gap> t:= CharTable( "J1" );;
    gap> SortClassesCharTable( t, ( 3, 4, 5, 6 ) );;
    gap> t.permutation;
    (3,4,5,6)
    gap> GetFusionMap( s, t );
    [ 1, 2, 4, 6, 5, 3, 10, 10 ]
    gap> s.fusions[5];
    rec(
      name := "J1",
      map := [ 1, 2, 3, 5, 4, 6, 10, 10 ],
      text :=
       "fusion is unique up to table automorphisms,\nthe representative is\
     equal to the fusion map on the CAS table" )