FUNCTION: LieTools/MixedTensor
USAGE: MixedTensor(part,hfw,Gt); MixedTensor(part,hfw); MixedTensor(part,hfw,Gtype,rnk);
SYNOPSIS: MixedTensor(part,hfw,Gt) computes the decomposition of the representation 
  in the tensor algebra of the f.d. representation of Gt with highest weight hfw 
  with symmetry corresponding to the partition part.
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE:
> T3 := TensorProduct([0,1],TensorProduct([0,1],[0,1],G2),G2);

  T3 := XX[0, 3] + 2 XX[3, 1] + 3 XX[2, 1] + 3 XX[0, 2] + 4 XX[3, 0]

         + 5 XX[0, 1] + XX[4, 0] + 2 XX[1, 1] + 3 XX[2, 0] + XX[1, 0]

         + XX[0, 0]

> S3 := SymTensor(3,[0,1],G2);

      S3 := XX[0, 3] + XX[2, 1] + XX[3, 0] + XX[0, 1] + XX[1, 0]

> A3 := AltTensor(3,[0,1],G2);

      A3 := XX[4, 0] + XX[0, 2] + XX[3, 0] + XX[2, 0] + XX[0, 0]

> P3 := MixedTensor([2,1],[0,1],G2);

  P3 := XX[3, 1] + XX[2, 1] + XX[0, 2] + XX[3, 0] + XX[1, 1]

         + XX[2, 0] + 2 XX[0, 1]

> T3 - S3 - A3 - 2*P3;

                                  0
 
SEE ALSO: LieTools[TensorProduct], LieTools[SymTensor], LieTools[AltTensor]
