GAP Manual: 51.24. FusionsAllowedByRestrictions

FusionsAllowedByRestrictions( subtbl, tbl, subchars, chars,
fus, parameters )

returns a list of (possibly parametrized, see More about Maps and Parametrized Maps) maps map which are contained in the parametrized map fus and which have the property that for all chi in the list chars of characters of the character table tbl, the restrictions [ chi_subtbl = CompositionMaps( chi, fus ) ] (see CompositionMaps) have nonnegative integral scalar products with all characters in the list subchars.

parameters must be a record with fields

maxlen:
an integer that controls the position where branches take place

contained:
a function, usually ContainedCharacters or ContainedPossibleCharacters; for a restriction rest, it returns the list contained( subtbl, subchars, rest );

minamb, maxamb:
two arbitrary objects; contained is called only for restrictions rest with minamb < Indeterminateness( rest ) < maxamb;

quick:
a boolean value; if it is true, the scalar products of uniquely determined restrictions are not checked.

fus will be improved, i.e. is changed by the algorithm.

If there is no character left which allows an immediate improvement but there are characters in chars with indeterminateness of the restrictions bigger than parameters.minamb, a branch is necessary. Two kinds of branches may occur: If parameters.contained( tbl, subchars, rest ) has length at most parameters.maxlen, the union of maps allowed by the characters in rest is computed; otherwise a suitable class c is taken which is significant for some character, and the union of all admissible maps with image x on c is computed, where x runs over fus[c].

    gap> s:= CharTable( "U3(3)" );; t:= CharTable( "J4" );;
    gap> fus:= InitFusion( s, t );;
    gap> TestConsistencyMaps( s.powermap, fus, t.powermap );;
    gap> ConsiderTableAutomorphisms( fus, t.automorphisms );; fus;
    [ 1, 2, 4, 4, [ 5, 6 ], [ 5, 6 ], [ 5, 6 ], 10, 12, [ 12, 13 ], 
      [ 14, 15, 16 ], [ 14, 15, 16 ], [ 21, 22 ], [ 21, 22 ] ]
    gap> FusionsAllowedByRestrictions( s, t, s.irreducibles,
    >             t.irreducibles, fus, rec( maxlen:= 10,
    >             contained:= ContainedPossibleCharacters,
    >             minamb:= 2, maxamb:= "infinity", quick:= false ) );
    [ [ 1, 2, 4, 4, 5, 5, 6, 10, 12, 13, 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 ] ]
    # cf.\ example in "SubgroupFusions"

FusionsAllowedByRestrictions is used by SubgroupFusions SubgroupFusions.