FUNCTION: LieTools/UgGenHWV
USAGE: UgGenHWV(upoly);
SYNOPSIS: UgGenHWV(upoly) finds a highest weight vector of the submodule
  of U[g] generated by adjoint action of g on upoly. Note: this routine
  simply applies the raising operators to upoly until they finally annihilate
  the result, and then returns to last nonzero element of U(g). 
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].). 
EXAMPLE: 
> with(LieTools):
> gSetup(A,2);
Setting up Gtype = A   rnk = 2
> upoly := u(g[4],g[5]);

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

> UgGenHWV(upoly);

                           2 u(g[8], g[8])

> 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],

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

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

         - 2/3 u(g[2], g[7]) - 2/3 u(g[3], g[6])]

SEE ALSO: LieTools[UgC2GenHWVs]
