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i1 : run "date";
Sun May 10 08:17:16 EDT 2026

i2 : needsPackage("LieAlgebraRepresentations");

i3 : sp6 = simpleLieAlgebra("C",3);

i4 : rhoV001 = deGraafRepresentation({0,0,1},sp6);
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
max-lev=14
Finished level 1. {#G,#B}={2, 2}
Finished level 2. {#G,#B}={4, 3}
Finished level 3. {#G,#B}={5, 5}
Finished level 4. {#G,#B}={7, 7}
Finished level 5. {#G,#B}={9, 9}
Finished level 6. {#G,#B}={12, 11}
Finished level 7. {#G,#B}={14, 12}
Finished level 8. {#G,#B}={16, 13}
Finished level 9. {#G,#B}={17, 14}
Finished level 10. {#G,#B}={18, 14}
Finished level 11. {#G,#B}={18, 14}
Finished level 12. {#G,#B}={18, 14}
Finished level 13. {#G,#B}={18, 14}
Finished level 14. {#G,#B}={18, 14}
Compute rho(B_0)
Compute rho(B_1)
Compute rho(B_2)
Compute rho(B_3)
Compute rho(B_4)
Compute rho(B_5)
Compute rho(B_6)
Compute rho(B_7)
Compute rho(B_8)
Compute rho(B_9)
Compute rho(B_10)
Compute rho(B_11)
Compute rho(B_12)
Compute rho(B_13)
Compute rho(B_14)
Compute rho(B_15)
Compute rho(B_16)
Compute rho(B_17)
Compute rho(B_18)
Compute rho(B_19)
Compute rho(B_20)

i5 : rhoV001star = dual rhoV001;

i6 : rhoW9V001star=exteriorPower(9,rhoV001star);

i7 : hwv = weightMuHighestWeightVectorsInW({5,0,0},rhoW9V001star);

              2002       1
o7 : Matrix QQ     <-- QQ

i8 : rhoV500 = deGraafRepresentation({5,0,0},sp6);
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
max-lev=30
Finished level 1. {#G,#B}={2, 2}
Finished level 2. {#G,#B}={3, 4}
Finished level 3. {#G,#B}={4, 7}
Finished level 4. {#G,#B}={4, 12}
Finished level 5. {#G,#B}={4, 19}
Finished level 6. {#G,#B}={5, 28}
Finished level 7. {#G,#B}={6, 39}
Finished level 8. {#G,#B}={8, 53}
Finished level 9. {#G,#B}={11, 69}
Finished level 10. {#G,#B}={16, 87}
Finished level 11. {#G,#B}={22, 106}
Finished level 12. {#G,#B}={31, 126}
Finished level 13. {#G,#B}={41, 146}
Finished level 14. {#G,#B}={54, 165}
Finished level 15. {#G,#B}={68, 183}
Finished level 16. {#G,#B}={84, 199}
Finished level 17. {#G,#B}={100, 213}
Finished level 18. {#G,#B}={118, 224}
Finished level 19. {#G,#B}={134, 233}
Finished level 20. {#G,#B}={150, 240}
Finished level 21. {#G,#B}={164, 245}
Finished level 22. {#G,#B}={177, 248}
Finished level 23. {#G,#B}={187, 250}
Finished level 24. {#G,#B}={196, 251}
Finished level 25. {#G,#B}={202, 252}
Finished level 26. {#G,#B}={207, 252}
Finished level 27. {#G,#B}={210, 252}
Finished level 28. {#G,#B}={212, 252}
Finished level 29. {#G,#B}={213, 252}
Finished level 30. {#G,#B}={214, 252}
Compute rho(B_0)
Compute rho(B_1)
Compute rho(B_2)
Compute rho(B_3)
Compute rho(B_4)
Compute rho(B_5)
Compute rho(B_6)
Compute rho(B_7)
Compute rho(B_8)
Compute rho(B_9)
Compute rho(B_10)
Compute rho(B_11)
Compute rho(B_12)
Compute rho(B_13)
Compute rho(B_14)
Compute rho(B_15)
Compute rho(B_16)
Compute rho(B_17)
Compute rho(B_18)
Compute rho(B_19)
Compute rho(B_20)

i9 : rhoV500 = lieAlgebraRepresentation(rhoV500#"Module",rhoV001#"Basis",rhoV500#"RepresentationMatrices");

i10 : V500InW9V001star=VInWedgekW(rhoV500,9,rhoV001star,hwv,"SaveAsFunction"=>"V500InW9V001star");
Length 1 complete. 5 new words found
Length 2 complete. 15 new words found
Length 3 complete. 35 new words found
Length 4 complete. 70 new words found
Length 5 complete. 126 new words found

i11 : hwv2 = weightMuHighestWeightVectorsInSymdW({2,0,0},2,rhoV500);
Constructing the Casimir operator...
Other EVs: {80, 62, 52, 48, 38, 36, 26, 16}
Beginning projections...
    j=0:
        EV 80 complete
        EV 62 complete
        EV 52 complete
        EV 48 complete
        EV 38 complete
        EV 36 complete
        EV 26 complete
        EV 16 complete
    #hwvs=0

i12 : rhoV200 = deGraafRepresentation({2,0,0},sp6);
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
max-lev=15
Finished level 1. {#G,#B}={2, 2}
Finished level 2. {#G,#B}={3, 4}
Finished level 3. {#G,#B}={5, 6}
Finished level 4. {#G,#B}={6, 9}
Finished level 5. {#G,#B}={8, 12}
Finished level 6. {#G,#B}={11, 15}
Finished level 7. {#G,#B}={15, 17}
Finished level 8. {#G,#B}={19, 19}
Finished level 9. {#G,#B}={24, 20}
Finished level 10. {#G,#B}={28, 21}
Finished level 11. {#G,#B}={32, 21}
Finished level 12. {#G,#B}={35, 21}
Finished level 13. {#G,#B}={37, 21}
Finished level 14. {#G,#B}={38, 21}
Finished level 15. {#G,#B}={39, 21}
Compute rho(B_0)
Compute rho(B_1)
Compute rho(B_2)
Compute rho(B_3)
Compute rho(B_4)
Compute rho(B_5)
Compute rho(B_6)
Compute rho(B_7)
Compute rho(B_8)
Compute rho(B_9)
Compute rho(B_10)
Compute rho(B_11)
Compute rho(B_12)
Compute rho(B_13)
Compute rho(B_14)
Compute rho(B_15)
Compute rho(B_16)
Compute rho(B_17)
Compute rho(B_18)
Compute rho(B_19)
Compute rho(B_20)

i13 : rhoV200 = lieAlgebraRepresentation(rhoV200#"Module",rhoV001#"Basis",rhoV200#"RepresentationMatrices");

i14 : V200inS2V500 = VInSymdW(rhoV200,2,rhoV500,hwv2_0,"SaveAsFunction"=>"V200inS2V500");
Length 1 complete. 5 new words found
Length 2 complete. 15 new words found
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i15 : hwv3 = weightMuHighestWeightVectorsInSymdW({0,0,0},2,rhoV200);
Constructing the Casimir operator...
Other EVs: {20, 14, 6}
Beginning projections...
    j=0:
        EV 20 complete
        EV 14 complete
        EV 6 complete
    #hwvs=0

i16 : rhoV000=trivialRepresentation(sp6);

i17 : rhoV000 = lieAlgebraRepresentation(rhoV000#"Module",rhoV001#"Basis",rhoV000#"RepresentationMatrices");

i18 : V000InS2V200=VInSymdW(rhoV000,2,rhoV200,hwv3_0,"SaveAsFunction"=>"V000InS2V200");
Length 1 complete. 0 new words found
0

i19 : run "date";
Sun May 10 08:18:29 EDT 2026

i20 :