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i1 : run "date";
Wed May  6 17:11:36 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 V00030 in W9W2Stdstar
     V00030 = irreducibleLieAlgebraModule({0,0,0,3,0},sl6);

i8 : LAB = rhoStd#"Basis";

i9 : L00030 = GTrepresentationMatrices(V00030);

i10 : rhoV00030 = lieAlgebraRepresentation(V00030,LAB,L00030);

i11 : -- Need a hwv for V00030 in W9W2Stdstar
      -- Relatively easy because the weight {0,0,0,3,0} subspace in W9W2Stdstar is one-dimensional
      wts = representationWeights(rhoW2Stdstar);

i12 : s9 = subsets(apply(#wts, i -> i),9);

i13 : t = first select(s9, s -> sum apply(s, j -> wts_j)=={0,0,0,3,0})

o13 = {6, 7, 8, 9, 10, 11, 12, 13, 14}

o13 : List

i14 : hwv1 = transpose matrix {apply(s9, s -> if s==t then 1/1 else 0/1)};

               5005       1
o14 : Matrix QQ     <-- QQ

i15 : time V00030inW9W2Stdstar = VInWedgekW(rhoV00030,9,rhoW2Stdstar,hwv1,"SaveAsFunction"=>"V00030inW9W2Stdstar");
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i16 : -- Step 3: Get the invariant in Sym3 V00030
      hwv2 = weightMuHighestWeightVectorsInSymdW({0,0,0,0,0},3,rhoV00030);
Constructing the Casimir operator...
Other EVs: {180, 148, 140, 138, 126, 120, 116, 110, 108, 104, 100, 98, 96, 94, 92, 90, 88, 84, 82, 78, 76, 74, 72, 70, 68, 64, 60, 56, 48, 40, 36, 28, 20}
Beginning projections...
    j=0:
        EV 180 complete
        EV 148 complete
        EV 140 complete
        EV 138 complete
        EV 126 complete
        EV 120 complete
        EV 116 complete
        EV 110 complete
        EV 108 complete
        EV 104 complete
        EV 100 complete
        EV 98 complete
        EV 96 complete
        EV 94 complete
        EV 92 complete
        EV 90 complete
        EV 88 complete
        EV 84 complete
        EV 82 complete
        EV 78 complete
        EV 76 complete
        EV 74 complete
        EV 72 complete
        EV 70 complete
        EV 68 complete
        EV 64 complete
        EV 60 complete
        EV 56 complete
        EV 48 complete
        EV 40 complete
        EV 36 complete
        EV 28 complete
        EV 20 complete
    #hwvs=0

i17 : rhoV00000=trivialRepresentation(sl6);

i18 : rhoV00000 = lieAlgebraRepresentation(rhoV00000#"Module",LAB,rhoV00000#"RepresentationMatrices");

i19 : V00000inS3V00030 = VInSymdW(rhoV00000,3,rhoV00030,hwv2_0,"SaveAsFunction"=>"V00000inS3V00030");
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0

i20 : run "date";
Thu May  7 09:32:40 EDT 2026

i21 :