FusionsAllowedByRestrictions( subtbl, tbl, subchars, chars,
fus, parameters )
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
:
contained
:contained( subtbl, subchars, rest )
;
minamb
, maxamb
:minamb < Indeterminateness( rest ) < maxamb
;
quick
: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
.
GAP 3.4.4