run "date";
needsPackage("LieAlgebraRepresentations");
so10 = simpleLieAlgebra("D",5);
rhoV00010 = deGraafRepresentation({0,0,0,1,0},so10);
rhoV00010star = dual rhoV00010;
LAB = rhoV00010#"Basis";
rhoV40000 = deGraafRepresentation({4,0,0,0,0},so10);
rhoV40000 = lieAlgebraRepresentation(rhoV40000#"Module",LAB,rhoV40000#"RepresentationMatrices");
wts = representationWeights(rhoV00010star);
s8 = subsets(apply(#wts, i -> i),8);
t=first select(s8, s -> sum apply(s, j -> wts_j)=={4,0,0,0,0})
hwv1 = transpose matrix {apply(s8, s -> if s==t then 1/1 else 0/1)};
V40000inW8V00010star = VInWedgekW(rhoV40000,8,rhoV00010star,hwv1,"SaveAsFunction"=>"V40000inW8V00010star");
hwv2 = weightMuHighestWeightVectorsInSymdW({0,0,0,0,0},2,rhoV40000);
rhoV00000=trivialRepresentation(so10);
rhoV00000 = lieAlgebraRepresentation(rhoV00000#"Module",LAB,rhoV00000#"RepresentationMatrices");
V00000InS2V40000=VInSymdW(rhoV00000,2,rhoV40000,hwv2_0,"SaveAsFunction"=>"V00000InS2V40000");
run "date";


quit