run "date";
needsPackage("LieAlgebraRepresentations");
so10 = simpleLieAlgebra("D",5);
rhoV00010 = deGraafRepresentation({0,0,0,1,0},so10);
rhoV00010star = dual rhoV00010;
LAB = rhoV00010#"Basis";
rhoV30001 = deGraafRepresentation({3,0,0,0,1},so10);
rhoV30001 = lieAlgebraRepresentation(rhoV30001#"Module",LAB,rhoV30001#"RepresentationMatrices");
wts = representationWeights(rhoV00010star);
s7 = subsets(apply(#wts, i -> i),7);
t=first select(s7, s -> sum apply(s, j -> wts_j)=={3,0,0,0,1})
hwv1 = transpose matrix {apply(s7, s -> if s==t then 1/1 else 0/1)};
V30001inW7V00010star = VInWedgekW(rhoV30001,7,rhoV00010star,hwv1,"SaveAsFunction"=>"V30001inW7V00010star");
run "date";
quit

run "date";
needsPackage("LieAlgebraRepresentations");
so10 = simpleLieAlgebra("D",5);
rhoV30001 = deGraafRepresentation({3,0,0,0,1},so10);
LAB = rhoV30001#"Basis";
rhoV30000 = deGraafRepresentation({3,0,0,0,0},so10);
rhoV30000 = lieAlgebraRepresentation(rhoV30000#"Module",rhoV30001#"Basis",rhoV30000#"RepresentationMatrices");
hwv2 = weightMuHighestWeightVectorsInSymdW({3,0,0,0,0},2,rhoV30001);
V30000inS2V30001 = VInSymdW(rhoV30000,2,rhoV30001,hwv2_0,"SaveAsFunction"=>"V30000inS2V30001");
run "date";
quit

run "date";
needsPackage("LieAlgebraRepresentations");
so10 = simpleLieAlgebra("D",5);
rhoV30000 = deGraafRepresentation({3,0,0,0,0},so10);
LAB = rhoV30000#"Basis";
rhoV00000=trivialRepresentation(so10);
rhoV00000 = lieAlgebraRepresentation(rhoV00000#"Module",LAB,rhoV00000#"RepresentationMatrices");
hwv3 = weightMuHighestWeightVectorsInSymdW({0,0,0,0,0},2,rhoV30000);
V00000InS2V30000=VInSymdW(rhoV00000,2,rhoV30000,hwv3_0,"SaveAsFunction"=>"V00000InS2V30000");
run "date";
quit