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i1 : run "date";
Fri May  8 05:33:53 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 V11011 in W9W2Stdstar
     V11011 = irreducibleLieAlgebraModule({1,1,0,1,1},sl6);

i8 : LAB = rhoStd#"Basis";

i9 : time L11011 = GTrepresentationMatrices(V11011);

i10 : rhoV11011 = lieAlgebraRepresentation(V11011,LAB,L11011);

i11 : -- Need a hwv for V11011 in W9W2Std
      -- Relatively easy because the weight {1,1,0,1,1} subspace in W9W2Std 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)=={1,1,0,1,1})

o13 = {5, 7, 8, 9, 10, 11, 12, 13, 14}

o13 : List

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

               5005       1
o14 : Matrix QQ     <-- QQ

i15 : time V11011inW9W2Stdstar = VInWedgekW(rhoV11011,9,rhoW2Stdstar,hwv,"SaveAsFunction"=>"V11011inW9W2Stdstar");
Length 1 complete. 14 new words found
Length 2 complete. 97 new words found
Length 3 complete. 415 new words found
Length 4 complete. 1104 new words found
Length 5 complete. 1368 new words found
Length 6 complete. 676 new words found

i16 : -- Step 3: Get the invariant in V11011 otimes V11011
      V00000inV11011otimesV11011 = gtInvariantInVtensorVdual({1,1,0,1,1});

i17 : fn = openOut "V00000inV11011otimesV11011.m2";

i18 : fn << "V00000inV11011otimesV11011 = (A,B) -> ";

i19 : fn << toString V00000inV11011otimesV11011 << endl;

i20 : close fn;

i21 : run "date";
Fri May  8 14:13:45 EDT 2026

i22 :