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AS defining char SU3 Dim 6
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SU3 Dim 6
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Anna Sucker committed Oct 6, 2021
1 parent 8427afc commit 32d9e46
Showing 1 changed file with 49 additions and 0 deletions.
49 changes: 49 additions & 0 deletions gap/AlmostSimpleDefiningCharacteristic.gi
Original file line number Diff line number Diff line change
Expand Up @@ -24,3 +24,52 @@ function(q)
fi;
return Group(Concatenation(MTX.Generators(MM),[S]));
end);

# Construction of group as in Table 5.6 row 5 from [BHR13]
BindGlobal("u3qdim6",
function(q)
local A, G, M, MM, S, T, general, normaliser, w;
general := ValueOption("general");
if general = fail then
general := false;
fi;
normaliser := ValueOption("normaliser");
if normaliser = fail then
normaliser := false;
fi;
Assert(1,IsOddInt(q));
if normaliser then
general := true;
fi;
w := PrimitiveElement(GF(q^2));
# rewritten select statement
if general then
G := GU(3,q);
else
G := SU(3,q);
fi;
M := GModuleByMats(GeneratorsOfGroup(G),GF(q^2));
T := TensorProductGModule(M,M);
MM := Filtered(MTX.CompositionFactors(T),c->MTX.Dimension(c) = 6)[1];
# A := ActionGroup(MM); -> A is MTX.Generators(MM)
# A := A^TransformForm(A); ??
A := Group(MTX.Generators(MM));
# change back fixed form into standard GAP form Antidiag(1, ..., 1)
SetInvariantSesquilinearForm(A, rec(matrix := MTX.InvariantBilinearForm(A)));
A := ConjugateToStandardForm(A, "U");
if not general then
# S := ScalarMat(6,(w^(q-1))^(QuoInt((q+1),Gcd(6,q+1))));
# return SubStructure(GL(6,q^2),A,#TODO CLOSURE
# S);
S := (w^(q-1))^(QuoInt((q+1),Gcd(6,q+1)))*IdentityMat(6,GF(q));
elif not normaliser then
# return SubStructure(GL(6,q^2),A,#TODO CLOSURE
# ScalarMat(6,w^(q-1)));
S := w^(q-1)*IdentityMat(6,GF(q));
else
S := w*IdentityMat(6,GF(q));
fi;
# return SubStructure(GL(6,q^2),A,#TODO CLOSURE
# ScalarMat(6,w));
return Group(GeneratorsOfGroup(A),[S]);
end);

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