AS defining char SU3 Dim 6

SU3 Dim 6

Author: Anna Sucker

gap/AlmostSimpleDefiningCharacteristic.gi

@@ -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);