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i1 : run "date";
Tue May  5 20:05:44 EDT 2026

i2 : needsPackage("LieAlgebraRepresentations");

i3 : sl6 = simpleLieAlgebra("A",5);

i4 : rhoStd = standardRepresentation(sl6);

i5 : rhoW2Std = exteriorPower(2,rhoStd);

i6 : rhoW2Stdstar = dual rhoW2Std;

i7 : -- Step 2: Get V02002 in W8W2Stdstar
     V02002 = irreducibleLieAlgebraModule({0,2,0,0,2},sl6);

i8 : LAB = rhoStd#"Basis";

i9 : time L02002 = GTrepresentationMatrices(V02002);

i10 : rhoV02002 = lieAlgebraRepresentation(V02002,LAB,L02002);

i11 : -- Need a hwv for V02002 in W8W2Stdstar
      -- Relatively easy because the weight {0,2,0,0,2} subspace in W8W2Stdstar is one-dimensional
      wts = representationWeights(rhoW2Stdstar);

i12 : s8 = subsets(apply(#wts, i -> i),8);

i13 : t = first select(s8, s -> sum apply(s, j -> wts_j)=={0,2,0,0,2})

o13 = {5, 8, 9, 10, 11, 12, 13, 14}

o13 : List

i14 : hwv = transpose matrix {apply(s8, s -> if s==t then 1/1 else 0/1)};

               6435       1
o14 : Matrix QQ     <-- QQ

i15 : VInWedgekW(rhoV02002,8,rhoW2Stdstar,hwv,"SaveAsFunction"=>"V02002inW8W2Stdstar");
Length 1 complete. 11 new words found
Length 2 complete. 66 new words found
Length 3 complete. 236 new words found
Length 4 complete. 586 new words found
Length 5 complete. 600 new words found
Length 6 complete. 300 new words found

i16 : -- Step 3: Get V02000 in Sym2 V02002
      V02000 = irreducibleLieAlgebraModule({0,2,0,0,0},sl6);

i17 : L02000 = GTrepresentationMatrices(V02000);

i18 : rhoV02000 = lieAlgebraRepresentation(V02000,LAB,L02000);

i19 : hwv2 = weightMuHighestWeightVectorsInSymdW({0,2,0,0,0},2,rhoV02002);
Constructing the Casimir operator...
Other EVs: {292/3, 256/3, 244/3, 232/3, 226/3, 220/3, 208/3, 196/3, 190/3, 184/3, 178/3, 172/3, 166/3, 160/3, 154/3, 148/3, 142/3, 136/3, 130/3, 124/3, 112/3, 100/3, 88/3}
Beginning projections...
    j=0:
        EV 292/3 complete
        EV 256/3 complete
        EV 244/3 complete
        EV 232/3 complete
        EV 226/3 complete
        EV 220/3 complete
        EV 208/3 complete
        EV 196/3 complete
        EV 190/3 complete
        EV 184/3 complete
        EV 178/3 complete
        EV 172/3 complete
        EV 166/3 complete
        EV 160/3 complete
        EV 154/3 complete
        EV 148/3 complete
        EV 142/3 complete
        EV 136/3 complete
        EV 130/3 complete
        EV 124/3 complete
        EV 112/3 complete
    j=1:
        EV 292/3 complete
        EV 256/3 complete
        EV 244/3 complete
        EV 232/3 complete
        EV 226/3 complete
        EV 220/3 complete
        EV 208/3 complete
        EV 196/3 complete
        EV 190/3 complete
        EV 184/3 complete
        EV 178/3 complete
        EV 172/3 complete
        EV 166/3 complete
        EV 160/3 complete
        EV 154/3 complete
        EV 148/3 complete
        EV 142/3 complete
        EV 136/3 complete
        EV 130/3 complete
        EV 124/3 complete
        EV 112/3 complete
    j=2:
        EV 292/3 complete
        EV 256/3 complete
        EV 244/3 complete
        EV 232/3 complete
        EV 226/3 complete
        EV 220/3 complete
        EV 208/3 complete
        EV 196/3 complete
        EV 190/3 complete
        EV 184/3 complete
        EV 178/3 complete
        EV 172/3 complete
        EV 166/3 complete
        EV 160/3 complete
        EV 154/3 complete
        EV 148/3 complete
        EV 142/3 complete
        EV 136/3 complete
        EV 130/3 complete
        EV 124/3 complete
        EV 112/3 complete
        EV 100/3 complete
        EV 88/3 complete
    #hwvs=0

i20 : VInSymdW(rhoV02000,2,rhoV02002,hwv2_0,"SaveAsFunction"=>"V02000inS2V02002");
Length 1 complete. 8 new words found
Length 2 complete. 36 new words found
Length 3 complete. 40 new words found
Length 4 complete. 20 new words found
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i21 : -- Step 4: Get the invariant in Sym3 V02000
      hwv3 = weightMuHighestWeightVectorsInSymdW({0,0,0,0,0},3,rhoV02000);
Constructing the Casimir operator...
Other EVs: {96, 76, 68, 60, 56, 48, 40, 36, 28, 20}
Beginning projections...
    j=0:
        EV 96 complete
        EV 76 complete
        EV 68 complete
        EV 60 complete
        EV 56 complete
        EV 48 complete
        EV 40 complete
        EV 36 complete
        EV 28 complete
        EV 20 complete
    #hwvs=0

i22 : rhoV00000=trivialRepresentation(sl6);

i23 : rhoV00000 = lieAlgebraRepresentation(rhoV00000#"Module",rhoV02000#"Basis",rhoV00000#"RepresentationMatrices");

i24 : V00000inS3V02000=VInSymdW(rhoV00000,3,rhoV02000,hwv3_0,"SaveAsFunction"=>"V00000inS3V02000");
Length 1 complete. 0 new words found
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i25 : run "date";
Wed May  6 00:38:47 EDT 2026

i26 :