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i1 : run "date";
Tue May  5 18:20:38 EDT 2026

i2 : needsPackage("LieAlgebraRepresentations");

i3 : sl6 = simpleLieAlgebra("A",5);

i4 : Std = standardModule(sl6);

i5 : peek Std

o5 = LieAlgebraModule{cache => CacheTable{}                                              }
                      DecompositionIntoIrreducibles => VirtualTally{{1, 0, 0, 0, 0} => 1}
                      LieAlgebra => sl6

i6 : W2Std=exteriorPower(2,Std);

i7 : W2Stdstar = dual W2Std;

i8 : peek W2Stdstar

o8 = LieAlgebraModule{cache => CacheTable{}                                              }
                      DecompositionIntoIrreducibles => VirtualTally{{0, 0, 0, 1, 0} => 1}
                      LieAlgebra => sl6

i9 : W8W2Stdstar=exteriorPower(8,W2Stdstar);

i10 : peek W8W2Stdstar

o10 = LieAlgebraModule{cache => CacheTable{}                                              }
                       DecompositionIntoIrreducibles => VirtualTally{{0, 2, 0, 0, 2} => 1}
                                                                     {1, 0, 0, 2, 1} => 1
                                                                     {2, 1, 0, 1, 0} => 1
                       LieAlgebra => sl6

i11 : dim irreducibleLieAlgebraModule(sl6,{2,1,0,1,0})

o11 = 2430

i12 : dim irreducibleLieAlgebraModule(sl6,{1,0,0,2,1})

o12 = 2205

i13 : dim irreducibleLieAlgebraModule(sl6,{0,2,0,0,2})

o13 = 1800

i14 : V02002 = irreducibleLieAlgebraModule(sl6,{0,2,0,0,2});

i15 : S2V02002=symmetricPower(2,V02002);

i16 : peek S2V02002

o16 = LieAlgebraModule{cache => CacheTable{}                                              }
                       DecompositionIntoIrreducibles => VirtualTally{{0, 0, 0, 2, 4} => 1}
                                                                     {0, 0, 0, 4, 0} => 1
                                                                     {0, 0, 1, 1, 3} => 1
                                                                     {0, 0, 1, 2, 1} => 1
                                                                     {0, 0, 2, 0, 2} => 2
                                                                     {0, 1, 0, 2, 0} => 1
                                                                     {0, 1, 1, 0, 1} => 1
                                                                     {0, 2, 0, 0, 0} => 1
                                                                     {0, 2, 0, 1, 4} => 1
                                                                     {0, 2, 0, 3, 0} => 1
                                                                     {0, 2, 1, 0, 3} => 1
                                                                     {0, 2, 1, 1, 1} => 1
                                                                     {0, 3, 0, 1, 0} => 1
                                                                     {0, 4, 0, 0, 4} => 1
                                                                     {0, 4, 0, 2, 0} => 1
                                                                     {1, 0, 1, 2, 2} => 1
                                                                     {1, 0, 2, 0, 3} => 1
                                                                     {1, 0, 2, 1, 1} => 1
                                                                     {1, 1, 0, 1, 3} => 1
                                                                     {1, 1, 0, 2, 1} => 1
                                                                     {1, 1, 1, 0, 2} => 2
                                                                     {1, 1, 1, 1, 0} => 1
                                                                     {1, 2, 0, 0, 1} => 1
                                                                     {1, 2, 1, 1, 2} => 1
                                                                     {1, 3, 0, 0, 3} => 1
                                                                     {1, 3, 0, 1, 1} => 1
                                                                     {2, 0, 0, 1, 2} => 1
                                                                     {2, 0, 1, 0, 1} => 1
                                                                     {2, 0, 2, 0, 4} => 1
                                                                     {2, 0, 2, 2, 0} => 1
                                                                     {2, 1, 1, 0, 3} => 1
                                                                     {2, 1, 1, 1, 1} => 1
                                                                     {2, 2, 0, 0, 2} => 2
                                                                     {3, 0, 1, 1, 0} => 1
                                                                     {3, 1, 0, 0, 1} => 1
                                                                     {4, 0, 0, 0, 0} => 1
                       LieAlgebra => sl6

i17 : V02000 = irreducibleLieAlgebraModule(sl6,{0,2,0,0,0});

i18 : S3V02000=symmetricPower(3,V02000);

i19 : peek S3V02000

o19 = LieAlgebraModule{cache => CacheTable{}                                              }
                       DecompositionIntoIrreducibles => VirtualTally{{0, 0, 0, 0, 0} => 1}
                                                                     {0, 0, 0, 3, 0} => 1
                                                                     {0, 0, 4, 0, 0} => 1
                                                                     {0, 1, 0, 1, 0} => 1
                                                                     {0, 2, 0, 2, 0} => 2
                                                                     {0, 3, 0, 0, 0} => 1
                                                                     {0, 4, 0, 1, 0} => 1
                                                                     {0, 6, 0, 0, 0} => 1
                                                                     {1, 0, 2, 0, 1} => 1
                                                                     {1, 1, 0, 1, 1} => 1
                                                                     {1, 2, 1, 1, 0} => 1
                                                                     {2, 0, 0, 0, 2} => 1
                                                                     {2, 0, 2, 1, 0} => 1
                                                                     {2, 1, 1, 0, 1} => 1
                                                                     {2, 2, 2, 0, 0} => 1
                                                                     {4, 0, 0, 2, 0} => 1
                       LieAlgebra => sl6

i20 : run "date";
Tue May  5 19:43:25 EDT 2026

i21 :