FUNCTION: LieTools/UgC2GenHWVs
USAGE: UgC2GenHWVs(upoly);
SYNOPSIS: UgC2GenHWVs(X) will find the highest weight vectors of the summands
  of U(g) that are generated by the adjoint action of g on an element upoly of
  U[g].
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
gSetup(A,2);Setting up Gtype = A   rnk = 2
> upoly := u(g[4],g[5]);

                        upoly := u(g[4], g[5])

> 
> UgC2GenHWVs(upoly);

  [[2, 2], 2 u(g[8], g[8])], [[1, 1], u(g[8]) - 2/3 u(g[4], g[8])

         - 2 u(g[6], g[7]) + 2/3 u(g[5], g[8])], [[0, 0],

        -2/3 u(g[1], g[8]) - 2/3 u(g[4]) - 2/3 u(g[5])

         - 2/3 u(g[3], g[6]) - 2/9 u(g[5], g[5]) - 2/9 u(g[4], g[5])

         - 2/9 u(g[4], g[4]) - 2/3 u(g[2], g[7])]

SEE ALSO: 
