FUNCTION: LieTools/SgMkHHWgtBasis
USAGE: SgMkHHWgtBasis(hfwgt,n); 
SYNOPSIS: SgMkHHWgtBasis(hfwgt,n) will construct a basis for the space of
  highest weight vectors of weight hfwgt in the space of homogeneous 
  polynomials of degree n that are annihilated by the Laplacian.
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(A,3):
Setting up Gtype = A   rnk = 3
> DecompSg(3);

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

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

> SgMkHWgtBasis([1,0,1],3);

       2                                   2               2
  {g[9]  g[15] + 16 g[13] g[5] g[14] + g[7]  g[15] - 4 g[8]  g[15]

         - 2 g[9] g[7] g[15] - 16 g[11] g[5] g[15]

         - 8 g[12] g[8] g[13] - 4 g[9] g[12] g[13]

         + 4 g[10] g[7] g[14] + 8 g[10] g[8] g[14]

         - 4 g[10] g[9] g[14] + 4 g[12] g[7] g[13]

                                       2
         + 16 g[11] g[10] g[12], 2 g[8]  g[15] - 6 g[13] g[5] g[14]

                                           2
         + 1/2 g[8] g[7] g[15] + g[1] g[15]  + 1/2 g[9] g[8] g[15]

         - 3/2 g[10] g[7] g[14] + g[2] g[14] g[15] + g[4] g[12] g[15]

         - 3 g[10] g[8] g[14] + g[10] g[6] g[15] + g[9] g[7] g[15]

         + g[3] g[13] g[15] + 7 g[11] g[5] g[15]

         - 3/2 g[12] g[7] g[13] - 6 g[11] g[10] g[12]

         + 3 g[12] g[8] g[13] + 3/2 g[9] g[12] g[13]

         + 3/2 g[10] g[9] g[14]}

> nops(%);

                                  2

> SgMkHHWgtBasis([1,0,1],3);

  [-34/5 g[12] g[8] g[13] + 68/5 g[11] g[10] g[12]

         + 17/5 g[12] g[7] g[13] + 68/5 g[13] g[5] g[14]

         + 17/5 g[10] g[7] g[14] + 34/5 g[10] g[8] g[14]

         + g[9] g[8] g[15] + 2 g[10] g[6] g[15]

         - 58/5 g[11] g[5] g[15] + g[8] g[7] g[15]

         - 6/5 g[9] g[7] g[15] + 2 g[4] g[12] g[15]

                                         2
         + 2 g[3] g[13] g[15] - 12/5 g[8]  g[15] + 2 g[2] g[14] g[15]

                   2
         + 8/5 g[9]  g[15] - 17/5 g[10] g[9] g[14]

                                           2                     2
         - 17/5 g[9] g[12] g[13] + 8/5 g[7]  g[15] + 2 g[1] g[15] ]

> nops(%);

                                  1


SEE ALSO: LieTools[SgMkHWgtBasis], LieTools[DecompHg]
