q-Clebsch-Gordan coefficients for rank two quantum groups

E. Ardonne, J.K. Slingerland,
Clebsch-Gordan and 6j-coefficients for rank two quantum groups,
arXiv:1004.5456

Display of qCG-coefficients

Manipulate[If[oldtype3≠type3,groupinit3[type3];j13={0,0};j23={0,0};j33={0,0};v=1;,,groupinit3[type3];];If[Not[MemberQ[fus3[j13,j23],j33]],j33=fus3[j13,j23][[1]];v=1;];If[v>nv3[j13,j23,j33][[-1]],v=1];If[show3>Length[weights3[j33]],show3=0];Column[{Row[{Style["Rows labeled by m1, columns by m2; m3=m1+m2"]}],Row[If[Length[nv3[j13,j23,j33]]>1,{Style["Vertex number = "],v,Style[" out of "],nv3[j13,j23,j33][[-1]],Style[" ways of fusing "],j13,Style[" with "],j23,Style[" into "],j33},{Style["No fusion multiplicity"]}]],If[show3==0,TableForm[Table[With[{mult=Count[weights3[j33][[All,1;;rank3]],(m1+m2)[[1;;rank3]]]},If[mult==0,".",If[mult==1,qCG3[j13,m1,j23,m2,j33,Table[If[i≤rank3,(m1+m2)[[i]],1],{i,1,rank3+1}],{v},q]/.{q->If[kinf3,1,Exp[2. Pi I/(4(k3+dcox3))]]},MatrixForm[Table[qCG3[j13,m1,j23,m2,j33,Table[If[i≤rank3,(m1+m2)[[i]],m],{i,1,rank3+1}],{v},q]/.{q->If[kinf3,1,Exp[2. Pi I/(4(k3+dcox3))]]},{m,1,mult}],TableDirections->Column]]]],{m1,weights3[j13]},{m2,weights3[j23]}]//Chop,TableHeadings->{displayweights[weights3[j13]],displayweights[weights3[j23]]}],TableForm[Table[If[(m1+m2)[[1;;rank3]]==weights3[j33][[show3,1;;rank3]],qCG3[j13,m1,j23,m2,j33,weights3[j33][[show3]],{v},q]/.{q->If[kinf3,1,Exp[2. Pi I/(4(k3+dcox3))]]},"."],{m1,weights3[j13]},{m2,weights3[j23]}]//Chop,TableHeadings->{displayweights[weights3[j13]],displayweights[weights3[j23]]}]]}],{{type3,1,""},{2->Style["su(3)_2"],1->Style["su(3)_3/Z_3"],3->Style["so(5)_1"],4->Style["G2_1"]}},{{j13,{1,1},"j1"},irrepss[type3]},{{j23,{1,1},"j2"},irrepss[type3]},{{j33,{1,1},"j3"},fus3[j13,j23]},{{v,1},nv3[j13,j23,j33]},Style["Display the following m3 value(s)"],{{show3,0,""},Prepend[Table[m33->displayweights[weights3[j33]][[m33]],{m33,1,Length[weights3[j33]]}],0->Style["All"]]},{{kinf3,False,"q"},{False->Exp[2 Pi I/kplusdcox3[type3]],True->1}},ControlType->SetterBar,ControlPlacement->Top,SaveDefinitions->True]

Initialization

Initialization for su(3)_2

su32init3:=With[{},
k3=2;
rank3=2;
dcox3=3;
Clear[n3,nv3,fus3,weights3,irreptonum3];
irreps3={{0,0},{1,0},{0,1},{2,0},{1,1},{0,2}};
numirreps3=Length[irreps3];
weights3[{0,0}]={{0,0,1}};
weights3[{1,0}]={{1,0,1},{-1,1,1},{0,-1,1}};
weights3[{0,1}]={{0,1,1},{1,-1,1},{-1,0,1}};
weights3[{1,1}]={{1,1,1},{-1,2,1},{2,-1,1},{0,0,1},{0,0,2},{-2,1,1},{1,-2,1},{-1,-1,1}};
weights3[{2,0}]={{2,0,1},{0,1,1},{-2,2,1},{1,-1,1},{-1,0,1},{0,-2,1}};
weights3[{0,2}]={{0,2,1},{1,0,1},{2,-2,1},{-1,1,1},{0,-1,1},{-2,0,1}};
n3[1]=IdentityMatrix[6];
n3[2]={{0,1,0,0,0,0},{0,0,1,1,0,0},{1,0,0,0,1,0},{0,0,0,0,1,0},{0,1,0,0,0,1},{0,0,1,0,0,0}};
n3[3]={{0,0,1,0,0,0},{1,0,0,0,1,0},{0,1,0,0,0,1},{0,1,0,0,0,0},{0,0,1,1,0,0},{0,0,0,0,1,0}};
n3[4]={{0,0,0,1,0,0},{0,0,0,0,1,0},{0,1,0,0,0,0},{0,0,0,0,0,1},{0,0,1,0,0,0},{1,0,0,0,0,0}};
n3[5]={{0,0,0,0,1,0},{0,1,0,0,0,1},{0,0,1,1,0,0},{0,0,1,0,0,0},{1,0,0,0,1,0},{0,1,0,0,0,0}};
n3[6]={{0,0,0,0,0,1},{0,0,1,0,0,0},{0,0,0,0,1,0},{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,0,1,0,0}};
Do[irreptonum3[irreps3[[i]]]=i,{i,1,numirreps3}];
Do[fus3[irreps3[[i]],irreps3[[j]]]=DeleteCases[Table[If[n3[i][[j,k]]>0,irreps3[[k]]],{k,1,numirreps3}],Null],{i,1,numirreps3},{j,1,numirreps3}];
Do[nv3[i,j,k]=Range[n3[irreptonum3[i]][[irreptonum3[j],irreptonum3[k]]]],{i,irreps3},{j,irreps3},{k,fus3[i,j]}];
qCGlist3=Flatten[Table[{j1,m1,j2,m2,j3,m3,{v}},{j1,irreps3},{j2,irreps3},{j3,fus3[j1,j2]},{v,nv3[j1,j2,j3]},{m3,weights3[j3]},{m1,weights3[j1]},{m2,Cases[weights3[j2],x_/;m1[[1;;2]]+x[[1;;2]]==m3[[1;;2]]]}],6];
qCGvalues3={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),1,(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),1,(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),1,((q^2)/(Sqrt[qn4[3,q]])),-(1/(Sqrt[qn4[3,q]])),(1/((q^2) (Sqrt[qn4[3,q]]))),1,1,1,(1/((Sqrt[2]) q (Sqrt[1+qn4[2,q]]))),(((1/q)+q)/((Sqrt[2]) (Sqrt[1+qn4[2,q]]))),(q/((Sqrt[2]) (Sqrt[1+qn4[2,q]]))),(1/((Sqrt[2]) q (Sqrt[-1+qn4[2,q]]))),((-(1/q)+q)/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]))),-(q/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]))),1,1,1,((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),-(((1/(q^3))-(q^3))/((Sqrt[2]) (Sqrt[1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),-((q (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),(((1/(q^3))+(q^3))/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),-((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),(((q^3) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((q^3) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[qn4[3,q]])/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[qn4[3,q]])/((q^2) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[3,q]]))/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((-(1/q)-q) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((((1/q)-q) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[qn4[3,q]])/((q^2) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[3,q]]))/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[qn4[3,q]])/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) (q^3) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) (q^3) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),((q (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-((q (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-(1/((q^2) qn4[2,q])),-(1/(qn4[2,q])),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(1/(qn4[2,q])),-((((1/q)-q) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),(((-(1/q)-q) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-(1/(qn4[2,q])),(1/(qn4[2,q])),((q^2)/(qn4[2,q])),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q qn4[2,q])),-((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q qn4[2,q])),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),((Sqrt[qn4[2,q]])/((q^2) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-((Sqrt[qn4[2,q]])/(Sqrt[qn4[4,q]])),(1/((q^3) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[4,q]])),-(1/(q (Sqrt[qn4[4,q]]))),(1/((q^3) (Sqrt[qn4[4,q]]))),1,1,1,((q^2)/(Sqrt[qn4[3,q]])),-(1/(Sqrt[qn4[3,q]])),(1/((q^2) (Sqrt[qn4[3,q]]))),1,1,1,(1/((Sqrt[2]) q (Sqrt[1+qn4[2,q]]))),(((1/q)+q)/((Sqrt[2]) (Sqrt[1+qn4[2,q]]))),(q/((Sqrt[2]) (Sqrt[1+qn4[2,q]]))),-(1/((Sqrt[2]) q (Sqrt[-1+qn4[2,q]]))),(((1/q)-q)/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]))),(q/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]))),1,1,1,(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),1,(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),1,(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),(1/(q (Sqrt[qn4[2,q]]))),(q/(Sqrt[qn4[2,q]])),1,((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),((Sqrt[qn4[2,q]])/((q^2) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-((Sqrt[qn4[2,q]])/(Sqrt[qn4[4,q]])),(1/((q^3) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[4,q]])),-(1/(q (Sqrt[qn4[4,q]]))),(1/((q^3) (Sqrt[qn4[4,q]]))),(((q^3) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(((q^3) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[qn4[3,q]])/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[qn4[3,q]])/((q^2) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[3,q]]))/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((-(1/q)-q) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((((1/q)-q) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[qn4[3,q]])/((q^2) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((q^2) (Sqrt[qn4[3,q]]))/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[qn4[3,q]])/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) (q^3) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[1+qn4[2,q]])/((Sqrt[2]) (q^3) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),((q (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),((q (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-(1/((q^2) qn4[2,q])),-(1/(qn4[2,q])),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),(1/(qn4[2,q])),-((((1/q)-q) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-(((-(1/q)-q) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) qn4[2,q])),-(1/(qn4[2,q])),(1/(qn4[2,q])),((q^2)/(qn4[2,q])),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q qn4[2,q])),((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q qn4[2,q])),(q/(Sqrt[qn4[2,q]])),-(1/(q (Sqrt[qn4[2,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),-(((1/(q^3))-(q^3))/((Sqrt[2]) (Sqrt[1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),((q (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),-(((1/(q^3))+(q^3))/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),1,1,1,1,1,1,((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),((-(1/(q^3))+(q^3))/((Sqrt[2]) (Sqrt[1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),-((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),((q (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q]]))),-(((1/(q^3))+(q^3))/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[3,q]]))),((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[3,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q]])),-(1/((q^2) (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),((q^2)/(Sqrt[qn4[3,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q]]))),(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[4,q]])),-(1/(q 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(Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(1/(q (Sqrt[qn4[4,q]]))),(1/((q^2) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(1/((q^4) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(1/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(((-(1/q)+q) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(((-(1/q)-q) (Sqrt[-1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),(1/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^4)/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(q/(Sqrt[qn4[4,q]])),-((q^2)/((Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),((Sqrt[1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-((Sqrt[-1+qn4[2,q]])/((Sqrt[2]) q (Sqrt[qn4[2,q]]) (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^4)/(Sqrt[1+qn4[5,q]])),-((q^2)/(Sqrt[1+qn4[5,q]])),(1/(Sqrt[1+qn4[5,q]])),(1/(Sqrt[1+qn4[5,q]])),-(1/((q^2) (Sqrt[1+qn4[5,q]]))),(1/((q^4) (Sqrt[1+qn4[5,q]]))),1,1,1,1,0,0,1,1,1,1,(((q^2) (Sqrt[qn4[3,q]]))/((Sqrt[qn4[2,q]]) 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Clear[qCG3];
Do[qCG3[Sequence@@qCGlist3[[i]],q]=qCGvalues3[[i]],{i,1,Length[qCGlist3]}];
]

Initialization for su(3)_3 / Z_3

su33init3:=With[{},
k3=3;
rank3=2;
dcox3=3;
Clear[n3,nv3,fus3,weights3,irreptonum3];
irreps3={{0,0},{1,1},{3,0},{0,3}};
numirreps3=Length[irreps3];
weights3[{0,0}]={{0,0,1}};
weights3[{1,1}]={{1,1,1},{-1,2,1},{2,-1,1},{0,0,1},{0,0,2},{-2,1,1},{1,-2,1},{-1,-1,1}};
weights3[{3,0}]={{3,0,1},{1,1,1},{-1,2,1},{2,-1,1},{-3,3,1},{0,0,1},{-2,1,1},{1,-2,1},{-1,-1,1},{0,-3,1}};
weights3[{0,3}]={{0,3,1},{1,1,1},{-1,2,1},{2,-1,1},{0,0,1},{3,-3,1},{-2,1,1},{1,-2,1},{-1,-1,1},{-3,0,1}};
n3[1]=IdentityMatrix[4];
n3[2]={{0,1,0,0},{1,2,1,1},{0,1,0,0},{0,1,0,0}};
n3[3]={{0,0,1,0},{0,1,0,0},{0,0,0,1},{1,0,0,0}};
n3[4]={{0,0,0,1},{0,1,0,0},{1,0,0,0},{0,0,1,0}};
Do[
irreptonum3[irreps3[[i]]]=i;
,{i,1,numirreps3}];
Do[fus3[irreps3[[i]],irreps3[[j]]]=DeleteCases[Table[If[n3[i][[j,k]]>0,irreps3[[k]]],{k,1,numirreps3}],Null],{i,1,numirreps3},{j,1,numirreps3}];
Do[nv3[i,j,k]=Range[n3[irreptonum3[i]][[irreptonum3[j],irreptonum3[k]]]],{i,irreps3},{j,irreps3},{k,fus3[i,j]}];
qCGlist3=Flatten[Table[{j1,m1,j2,m2,j3,m3,{v}},{j1,irreps3},{j2,irreps3},{j3,fus3[j1,j2]},{v,nv3[j1,j2,j3]},{m3,weights3[j3]},{m1,weights3[j1]},{m2,Cases[weights3[j2],x_/;m1[[1;;2]]+x[[1;;2]]==m3[[1;;2]]]}],6];
qCGvalues3={1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,((q^4)/(Sqrt[qn4[2,q] qn4[4,q]])),-((q^2)/(Sqrt[qn4[2,q] qn4[4,q]])),-((q^2)/(Sqrt[qn4[2,q] qn4[4,q]])),(1/(Sqrt[qn4[2,q] qn4[4,q]])),0,0,(1/(Sqrt[qn4[2,q] qn4[4,q]])),-(1/((q^2) (Sqrt[qn4[2,q] qn4[4,q]]))),-(1/((q^2) (Sqrt[qn4[2,q] qn4[4,q]]))),(1/((q^4) (Sqrt[qn4[2,q] qn4[4,q]]))),((q^3)/(Sqrt[1+qn4[4,q]])),0,-((Sqrt[((1+qn4[2,q])/(1+qn4[4,q]))])/(Sqrt[2])),-((Sqrt[((1+qn4[2,q])/(1+qn4[4,q]))])/(Sqrt[2])),(1/((q^3) (Sqrt[1+qn4[4,q]]))),0,(((q^2) (Sqrt[((1+qn4[2,q])/(1+qn4[4,q]))]))/(Sqrt[2])),((-(1/q)-q+(q^3))/(2 (Sqrt[1+qn4[4,q]]))),-(1/2) q (Sqrt[((qn4[3,q])/(1+qn4[4,q]))]),(((1/(q^3))-(1/q)-q)/(2 (Sqrt[1+qn4[4,q]]))),-((Sqrt[((qn4[3,q])/(1+qn4[4,q]))])/(2 q)),((Sqrt[((1+qn4[2,q])/(1+qn4[4,q]))])/((Sqrt[2]) (q^2))),(((q^2) (Sqrt[((1+qn4[2,q])/(1+qn4[4,q]))]))/(Sqrt[2])),((-(1/q)-q+(q^3))/(2 (Sqrt[1+qn4[4,q]]))),(1/2) q (Sqrt[((qn4[3,q])/(1+qn4[4,q]))]),(((1/(q^3))-(1/q)-q)/(2 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(Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-((Sqrt[qn4[2,q]])/((q^4) (Sqrt[qn4[3,q] qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),(1/(q (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^5)/(Sqrt[qn4[3,q] qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),-(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/((q^2) (Sqrt[qn4[3,q] qn4[4,q]]))),(1/(q (Sqrt[qn4[4,q]]))),-(1/((q^5) (Sqrt[qn4[3,q] qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(1/(q (Sqrt[qn4[3,q] qn4[4,q]]))),-(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/((q^2) (Sqrt[qn4[3,q] qn4[4,q]]))),(q/(Sqrt[qn4[3,q] qn4[4,q]])),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-((q^3)/(Sqrt[qn4[3,q] qn4[4,q]])),(1/((q^3) (Sqrt[qn4[3,q] qn4[4,q]]))),((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),(1/(q (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^6)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-((q^4)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),((q^2)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),((q^2)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-(1/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-(1/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),(1/((q^2) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),(1/((q^2) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),-(1/((q^4) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),(1/((q^6) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),1,1,1,1,1,1,1,1,1,1,(((q^3) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[5,q]])),-(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),((Sqrt[qn4[2,q]])/((q^3) (Sqrt[qn4[3,q] qn4[5,q]]))),((Sqrt[qn4[2,q]])/((q^3) (Sqrt[qn4[3,q] qn4[5,q]]))),-(1/((q^6) (Sqrt[qn4[3,q] qn4[5,q]]))),(((q^3) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[5,q]])),-((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[3,q] qn4[5,q]]))),-(((1-(1/(q^2))) (Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((1+(1/(q^2))) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(1/((q^2) (Sqrt[qn4[3,q] qn4[5,q]]))),-((Sqrt[qn4[2,q]])/((q^5) (Sqrt[qn4[3,q] qn4[5,q]]))),(((q^5) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),-(((q^2) (Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((q^2) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(1/((q^2) (Sqrt[qn4[3,q] qn4[5,q]]))),((Sqrt[qn4[2,q]])/(q (Sqrt[qn4[5,q]]))),-((Sqrt[qn4[2,q]])/((q^5) (Sqrt[qn4[3,q] qn4[5,q]]))),(((q^4) (Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((-1+(q^6)) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[1+qn4[2,q]]) (Sqrt[qn4[3,q] qn4[5,q]]))),-(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),-((-(1/(q^4))-(1/(q^2))+(q^2)+(q^4))/(2 (Sqrt[qn4[3,q] qn4[5,q]]))),((qn4[2,q])/(2 (Sqrt[qn4[5,q]]))),-(((-1+(1/(q^6))) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[1+qn4[2,q]]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),-(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (q^4) (Sqrt[qn4[3,q] qn4[5,q]]))),-(((q^4) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((1+(q^6)) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),-((qn4[2,q])/(2 (Sqrt[qn4[5,q]]))),((-(1/(q^4))+(1/(q^2))-(q^2)+(q^4))/(2 (Sqrt[qn4[3,q] qn4[5,q]]))),(((1+(1/(q^6))) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),-(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (q^4) (Sqrt[qn4[3,q] qn4[5,q]]))),(((q^5) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),-((q^2)/(Sqrt[qn4[3,q] qn4[5,q]])),(((1-(q^2)) (Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((1+(q^2)) (Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),-((Sqrt[qn4[2,q]])/((q^3) (Sqrt[qn4[5,q]]))),(((q^5) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),-((q^2)/(Sqrt[qn4[3,q] qn4[5,q]])),-((q (Sqrt[qn4[2,q]]))/(Sqrt[qn4[5,q]])),(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (q^2) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (q^2) (Sqrt[qn4[3,q] qn4[5,q]]))),-((Sqrt[qn4[2,q]])/((q^5) (Sqrt[qn4[3,q] qn4[5,q]]))),((q^6)/(Sqrt[qn4[3,q] qn4[5,q]])),-(((q^3) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),-(((q^3) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[5,q]])),(((Sqrt[qn4[2,q]]) (Sqrt[1+qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),(((Sqrt[-1+qn4[2,q]]) (Sqrt[qn4[2,q]]))/((Sqrt[2]) (Sqrt[qn4[3,q] qn4[5,q]]))),-((Sqrt[qn4[2,q]])/((q^3) (Sqrt[qn4[5,q]]))),((q^6)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-((q^4)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),((q^2)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),((q^2)/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-(1/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),-(1/(Sqrt[(-1+qn4[3,q]) qn4[5,q]])),(1/((q^2) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),(1/((q^2) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),-(1/((q^4) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),(1/((q^6) (Sqrt[(-1+qn4[3,q]) qn4[5,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),(1/(q (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-((q^3)/(Sqrt[qn4[3,q] qn4[4,q]])),(1/((q^3) (Sqrt[qn4[3,q] qn4[4,q]]))),((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(1/(q (Sqrt[qn4[3,q] qn4[4,q]]))),-(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/((q^2) (Sqrt[qn4[3,q] qn4[4,q]]))),(q/(Sqrt[qn4[3,q] qn4[4,q]])),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^5)/(Sqrt[qn4[3,q] qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),-(((q^2) (Sqrt[qn4[2,q]]))/(Sqrt[qn4[3,q] 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qn4[4,q]]))),-(1/((q^5) (Sqrt[qn4[3,q] qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),(1/((q^3) (Sqrt[qn4[3,q] qn4[4,q]]))),-((q^3)/(Sqrt[qn4[3,q] qn4[4,q]])),((Sqrt[qn4[2,q]])/(Sqrt[qn4[3,q] qn4[4,q]])),-(1/((q^3) (Sqrt[qn4[4,q]]))),((q^3)/(Sqrt[qn4[4,q]])),-(q/(Sqrt[qn4[4,q]])),(1/(q (Sqrt[qn4[4,q]]))),-(1/((q^3) (Sqrt[qn4[4,q]])))};
Clear[qCG3];
Do[qCG3[Sequence@@qCGlist3[[i]],q]=qCGvalues3[[i]],{i,1,Length[qCGlist3]}];
]

Initialization for so(5)_1

so51init3:=With[{},
k3=1;
rank3=2;
dcox3=3;
Clear[n3,nv3,fus3,weights3,irreptonum3];
irreps3={{0,0},{0,1},{1,0}};
numirreps3=Length[irreps3];
weights3[{0,0}]={{0,0,1}};
weights3[{0,1}]={{0,1,1},{1,-1,1},{-1,1,1},{0,-1,1}};
weights3[{1,0}]={{1,0,1},{-1,2,1},{0,0,1},{1,-2,1},{-1,0,1}};
n3[1]=IdentityMatrix[3];
n3[2]={{0,1,0},{1,0,1},{0,1,0}};
n3[3]={{0,0,1},{0,1,0},{1,0,0}};
Do[
irreptonum3[irreps3[[i]]]=i;
,{i,1,numirreps3}];
Do[fus3[irreps3[[i]],irreps3[[j]]]=DeleteCases[Table[If[n3[i][[j,k]]>0,irreps3[[k]]],{k,1,numirreps3}],Null],{i,1,numirreps3},{j,1,numirreps3}];
Do[nv3[i,j,k]=Range[n3[irreptonum3[i]][[irreptonum3[j],irreptonum3[k]]]],{i,irreps3},{j,irreps3},{k,fus3[i,j]}];
qCGlist3=Flatten[Table[{j1,m1,j2,m2,j3,m3,{v}},{j1,irreps3},{j2,irreps3},{j3,fus3[j1,j2]},{v,nv3[j1,j2,j3]},{m3,weights3[j3]},{m1,weights3[j1]},{m2,Cases[weights3[j2],x_/;m1[[1;;2]]+x[[1;;2]]==m3[[1;;2]]]}],6];
qCGvalues3={1,1,1,1,1,1,1,1,1,1,1,1,1,1,((q^2)/(Sqrt[-1+qn4[5,2,q]])),-(q/(Sqrt[-1+qn4[5,2,q]])),(1/(q (Sqrt[-1+qn4[5,2,q]]))),-(1/((q^2) (Sqrt[-1+qn4[5,2,q]]))),((Sqrt[q])/(Sqrt[qn4[2,2,q]])),-(1/((Sqrt[q]) (Sqrt[qn4[2,2,q]]))),((Sqrt[q])/(Sqrt[qn4[2,2,q]])),-(1/((Sqrt[q]) (Sqrt[qn4[2,2,q]]))),(1/(qn4[2,2,q])),(q/(qn4[2,2,q])),-(1/(q qn4[2,2,q])),-(1/(qn4[2,2,q])),((Sqrt[q])/(Sqrt[qn4[2,2,q]])),-(1/((Sqrt[q]) (Sqrt[qn4[2,2,q]]))),((Sqrt[q])/(Sqrt[qn4[2,2,q]])),-(1/((Sqrt[q]) (Sqrt[qn4[2,2,q]]))),((q^2)/(Sqrt[qn4[5,2,q]])),-(((Sqrt[q]) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-(1/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-(1/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-((Sqrt[qn4[2,2,q]])/((Sqrt[q]) (Sqrt[qn4[5,2,q]]))),(1/((q^2) (Sqrt[qn4[5,2,q]]))),1,1,1,1,1,(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-((Sqrt[qn4[2,2,q]])/((Sqrt[q]) (Sqrt[qn4[5,2,q]]))),(1/((q^2) (Sqrt[qn4[5,2,q]]))),(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-(1/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),(((q^(3/2)) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),-(1/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),((q^2)/(Sqrt[qn4[5,2,q]])),-(((Sqrt[q]) (Sqrt[qn4[2,2,q]]))/(Sqrt[qn4[5,2,q]])),((Sqrt[qn4[2,2,q]])/((q^(3/2)) (Sqrt[qn4[5,2,q]]))),((q^3)/(Sqrt[1+qn4[4,q]])),-(q/(Sqrt[1+qn4[4,q]])),(1/(Sqrt[1+qn4[4,q]])),-(1/(q (Sqrt[1+qn4[4,q]]))),(1/((q^3) (Sqrt[1+qn4[4,q]])))};
Clear[qCG3];
Do[qCG3[Sequence@@qCGlist3[[i]],q]=qCGvalues3[[i]],{i,1,Length[qCGlist3]}];
]

Initialization for G2_1

g21init3:=With[{},
k3=1;
rank3=2;
dcox3=4;
Clear[n3,nv3,fus3,weights3,irreptonum3];
irreps3={{0,0},{0,1}};
numirreps3=Length[irreps3];
weights3[{0,0}]={{0,0,1}};
weights3[{0,1}]={{0,1,1},{1,-1,1},{-1,2,1},{0,0,1},{1,-2,1},{-1,1,1},{0,-1,1}};
n3[1]=IdentityMatrix[2];
n3[2]={{0,1},{1,1}};
Do[
irreptonum3[irreps3[[i]]]=i;
,{i,1,numirreps3}];
Do[fus3[irreps3[[i]],irreps3[[j]]]=DeleteCases[Table[If[n3[i][[j,k]]>0,irreps3[[k]]],{k,1,numirreps3}],Null],{i,1,numirreps3},{j,1,numirreps3}];
Do[nv3[i,j,k]=Range[n3[irreptonum3[i]][[irreptonum3[j],irreptonum3[k]]]],{i,irreps3},{j,irreps3},{k,fus3[i,j]}];
qCGlist3=Flatten[Table[{j1,m1,j2,m2,j3,m3,{v}},{j1,irreps3},{j2,irreps3},{j3,fus3[j1,j2]},{v,nv3[j1,j2,j3]},{m3,weights3[j3]},{m1,weights3[j1]},{m2,Cases[weights3[j2],x_/;m1[[1;;2]]+x[[1;;2]]==m3[[1;;2]]]}],6];
qCGvalues3={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,((q^(10/3))/(Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]])),-((q^(8/3))/(Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]])),((q^(2/3))/(Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]])),-(1/(Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]])),(1/((q^(2/3)) (Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]]))),-(1/((q^(8/3)) (Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]]))),(1/((q^(10/3)) (Sqrt[qn4[3,3,q]-qn4[7,3,q]+qn4[11,3,q]]))),((q^2)/(Sqrt[-1+qn4[7,3,q]])),-((q (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),((Sqrt[qn4[2,3,q]])/(q (Sqrt[-1+qn4[7,3,q]]))),-(1/((q^2) (Sqrt[-1+qn4[7,3,q]]))),(((q^(5/3)) (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),-((q^(2/3))/(Sqrt[-1+qn4[7,3,q]])),(1/((q^(2/3)) (Sqrt[-1+qn4[7,3,q]]))),-((Sqrt[qn4[2,3,q]])/((q^(5/3)) (Sqrt[-1+qn4[7,3,q]]))),(((q^(5/3)) (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),-((q^(2/3))/(Sqrt[-1+qn4[7,3,q]])),(1/((q^(2/3)) (Sqrt[-1+qn4[7,3,q]]))),-((Sqrt[qn4[2,3,q]])/((q^(5/3)) (Sqrt[-1+qn4[7,3,q]]))),((q^(4/3))/(Sqrt[-1+qn4[7,3,q]])),((q^2)/(Sqrt[-1+qn4[7,3,q]])),-(1/(Sqrt[-1+qn4[7,3,q]])),(((1/(q^(2/3)))-(q^(2/3)))/(Sqrt[-1+qn4[7,3,q]])),(1/(Sqrt[-1+qn4[7,3,q]])),-(1/((q^2) (Sqrt[-1+qn4[7,3,q]]))),-(1/((q^(4/3)) (Sqrt[-1+qn4[7,3,q]]))),(((q^(5/3)) (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),-((q^(2/3))/(Sqrt[-1+qn4[7,3,q]])),(1/((q^(2/3)) (Sqrt[-1+qn4[7,3,q]]))),-((Sqrt[qn4[2,3,q]])/((q^(5/3)) (Sqrt[-1+qn4[7,3,q]]))),(((q^(5/3)) (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),-((q^(2/3))/(Sqrt[-1+qn4[7,3,q]])),(1/((q^(2/3)) (Sqrt[-1+qn4[7,3,q]]))),-((Sqrt[qn4[2,3,q]])/((q^(5/3)) (Sqrt[-1+qn4[7,3,q]]))),((q^2)/(Sqrt[-1+qn4[7,3,q]])),-((q (Sqrt[qn4[2,3,q]]))/(Sqrt[-1+qn4[7,3,q]])),((Sqrt[qn4[2,3,q]])/(q (Sqrt[-1+qn4[7,3,q]]))),-(1/((q^2) (Sqrt[-1+qn4[7,3,q]])))};
Clear[qCG3];
Do[qCG3[Sequence@@qCGlist3[[i]],q]=qCGvalues3[[i]],{i,1,Length[qCGlist3]}];
]

General

qn4[n_,q_]:=Sum[q^(4((n+1)/2-i)),{i,1,n}];
qn4[n_,d_,q_]:=Sum[q^(4/d((n+1)/2-i)),{i,1,n}];

groupinit3[type_]:=With[{},
If[Not[oldtype3==type],
Piecewise[{{su33init3,type==1},{su32init3,type==2},{so51init3,type==3},{g21init3,type==4}}];oldtype3=type;]
];

irrepss[type_]:=Piecewise[{{{{0,0},{1,1},{3,0},{0,3}},type==1},{{{0,0},{1,0},{0,1},{2,0},{1,1},{0,2}},type==2},{{{0,0},{0,1},{1,0}},type==3},{{{0,0},{0,1}},type==4}}]
kplusdcox3[type_]:=Piecewise[{{6,type==1},{5,type==2},{4,type==3},{5,type==4}}];

displayweights[weightvec_]:=Table[If[Count[weightvec,x_/;x[[1;;rank3]]==weightvec[[i,1;;rank3]]]==1,weightvec[[i,1;;rank3]],Append[weightvec[[i,1;;rank3]],{weightvec[[i,-1]]}]],{i,1,Length[weightvec]}]

Start

oldtype3=0;
groupinit3[1];
type3=1;