LieAlgebraModuleFromWeights -- finds a Lie algebra module based on its weights

i1 : g=simpleLieAlgebra("A",2);

i2 : U=irreducibleLieAlgebraModule({1,1},g);

i3 : M=U**U

o3 = M

o3 : LieAlgebraModule over g

i4 : T=weightDiagram M

o4 = VirtualTally{{-1, -1} => 6}
                  {-1, 2} => 6
                  {-2, -2} => 1
                  {-2, 1} => 6
                  {-2, 4} => 1
                  {-3, 0} => 2
                  {-3, 3} => 2
                  {-4, 2} => 1
                  {0, -3} => 2
                  {0, 0} => 10
                  {0, 3} => 2
                  {1, -2} => 6
                  {1, 1} => 6
                  {2, -1} => 6
                  {2, -4} => 1
                  {2, 2} => 1
                  {3, -3} => 2
                  {3, 0} => 2
                  {4, -2} => 1

o4 : VirtualTally

i5 : LieAlgebraModuleFromWeights(T,g)

o5 = M

o5 : LieAlgebraModule over g