FUNCTION: LieTools/SgDiagC2onZWS
USAGE: SgDiagC2onZWS(n);
SYNOPSIS: SgDiagC2onZWS(n) finds the eigenvectors and eigenvalues of the 2nd
  order Casimir on the space of homogeneous polynomials of degree n and weight zero. 
  The output is a list
     [monoset,[eval1,mult1,[ev11,ev12...]],[eval2,mult2,[ev21,ev22,...]],...]
  Here 
     monoset; monomial basis for zero weight space
     eval1 : first eigenvalue of the Casimir
     mult1 : multiplicity of the first eigenvalue
      ev11 : list of numerical coefficients of the first eigenvector with 
             eigenvalue eval1 with respect to the monomial basis monoset.
   etc.. 
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(G,2);
Setting up Gtype = G   rnk = 2
> SgDiagC2onZWS(2);

  [{g[10] g[5], g[8] g[7], g[6] g[9], g[3] g[12], g[2] g[13],

                                    2      2
        g[1] g[14], g[4] g[11], g[7] , g[8] },

        [0, 1, {[3, 3, 1, 1, 3, 3, 1, 1, 3]}], [7/6, 3, {

        [9/4, -27/4, 1, 0, 9/4, -27/4, 0, -5/4, -27/4],

        [-27/4, 21/4, 0, 1, 9/4, 9/4, 0, 7/4, 9/4],

        [9/4, -3/4, 0, 0, -27/4, 9/4, 1, -5/4, 9/4]}], [5/2, 5, {

        [-2, -1, -1, 1, -1, 0, 0, 0, 0],

        [-3, -1, 0, 0, -1, 1, 0, 0, 0],

        [-3, -1, -1, 0, 0, 0, 1, 0, 0], [2, 2, 0, 0, -2, 0, 0, 1, 0],

        [-2, 0, 0, 0, 0, 0, 0, 0, 1]}]]

SEE ALSO: 
