ContainedSpecialVectors( tbl, chars, parachar, func )
returns the list of all elements vec of the parametrized character
parachar (see More about Maps and Parametrized Maps), that have
integral norm and integral scalar product with the principal character of
the character table tbl and that satisfy func( tbl, chars, vec
)
, i.e., for that true
is returned.
gap> s:= CharTable( "HSM12" );; hs:= CharTable( "HS" );; gap> fus:= InitFusion( s, hs );; gap> rest:= CompositionMaps( hs.irreducibles[8], fus );; # no further condition\: gap> ContainedSpecialVectors( s, s.irreducibles, rest, > function(tbl,chars,vec) return true; end );; gap> Length( last ); 24 # better filter\:\ those with integral scalar products gap> ContainedSpecialVectors( s, s.irreducibles, rest, > IntScalarProducts ); [ [ 231, 7, -9, -9, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ], [ 231, 7, -9, 7, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ], [ 231, 7, -9, -9, 6, 15, 15, 15, 15, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ], [ 231, 7, -9, 7, 6, 15, 15, 15, 15, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ] ] # better filter\:\ the scalar products must be nonnegative gap> ContainedSpecialVectors( s, s.irreducibles, rest, > NonnegIntScalarProducts ); [ [ 231, 7, -9, -9, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ], [ 231, 7, -9, 7, 6, 15, 15, -1, -1, 1, 6, 6, 1, 1, -2, 1, 2, 2, 0, 0, 1, 0, 0, 0, 0 ] ]
Special cases of ContainedSpecialVectors
are
ContainedPossibleCharacters ContainedPossibleCharacters
and
ContainedPossibleVirtualCharacters
ContainedPossibleVirtualCharacters
.
ContainedSpecialVectors
successively examines all vectors contained in
parachar, thus it might not be useful if the indeterminateness exceeds
10^6. For another strategy that works for rational characters only,
see ContainedDecomposables.
GAP 3.4.4