FUNCTION: LieTools/SgMkRepWgtBasis
USAGE: SgMkRepWgtBasis(hfwgt,n);
SYNOPSIS: SgMkRepWgtBasis(hfwgt,n) will construct a basis for a finite
  dimensional representation with highest weight hfwgt in the 
  space of harmonic, homogeneous polynomials of degree n.
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(A,2):
Setting up Gtype = G   rnk = 2
> DecompHg(2);

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

> SgMkRepWgtBasis([2,0],2);

                                        2
  [-3 g[14] g[9] - 3 g[13] g[11] + g[12] ,

        g[13] g[10] - 1/3 g[14] g[7] - 1/9 g[12] g[11],

        g[5] g[14] - 1/3 g[13] g[7] - g[8] g[13] + 1/9 g[9] g[12],

                                            2
        g[12] g[10] - g[14] g[6] - 1/3 g[11] ,

        g[4] g[14] + g[12] g[8] + g[6] g[13] - 2/3 g[9] g[11],

        g[12] g[7] - 3 g[6] g[13] + g[9] g[11],

        g[10] g[9] - 1/2 g[11] g[8] - 1/6 g[6] g[12] + 1/2 g[3] g[14]

        ,

        g[11] g[7] + 3/2 g[11] g[8] - 1/2 g[6] g[12] - 3/2 g[3] g[14]

                                            2
        , g[4] g[13] + g[12] g[5] + 1/3 g[9] ,

        g[4] g[12] + 2 g[9] g[7] + 3 g[9] g[8] + 3 g[3] g[13],

        g[11] g[5] - 1/3 g[9] g[7] - g[3] g[13],

        g[10] g[7] + 3/2 g[10] g[8] - 1/6 g[6] g[11] + 3/2 g[2] g[14]

                               2                       2
        , g[1] g[14] + 1/9 g[7]  + 5/6 g[8] g[7] + g[8]

         - 1/6 g[6] g[9] - 1/18 g[3] g[12] - 1/2 g[2] g[13],

                         2
        g[4] g[11] - g[7]  - 3/2 g[8] g[7] + 1/2 g[6] g[9]

                                                                 2
         + 1/2 g[3] g[12] - 9/2 g[2] g[13], g[10] g[5] - 2/9 g[7]

         - 1/2 g[8] g[7] - 1/18 g[6] g[9] - 1/6 g[3] g[12]

         - 1/2 g[2] g[13],

        g[1] g[13] - 1/9 g[4] g[9] + 2/3 g[7] g[5] + g[8] g[5],

        g[10] g[4] + 1/2 g[8] g[6] + 1/6 g[3] g[11] - 1/2 g[2] g[12],

        g[7] g[6] + 3/2 g[8] g[6] + 1/2 g[3] g[11] + 3/2 g[2] g[12],

        g[1] g[12] - g[8] g[4] + 2 g[5] g[6] - 1/3 g[9] g[3],

        -g[9] g[3] + g[4] g[7] + 3 g[5] g[6],

                             2
        g[3] g[10] + 1/3 g[6]  + g[2] g[11],

        g[1] g[11] + 2/3 g[7] g[3] + g[3] g[8] - g[2] g[9],

        g[6] g[4] + g[7] g[3] - 3 g[2] g[9],

                            2
        g[1] g[9] + 1/3 g[4]  - g[3] g[5],

        g[1] g[10] - 1/3 g[2] g[7] - g[2] g[8] + 1/9 g[3] g[6],

        g[1] g[7] + 1/3 g[3] g[4] - 3 g[2] g[5],

                                        2
        g[1] g[6] + g[2] g[4] - 1/3 g[3] ]

SEE ALSO: 
