FUNCTION: LieTools/DiagC2onSgPolys
USAGE: DiagC2OnSgPolys(plist);
SYNOPSIS: This is a routine to find the eigenvalues and eigenvectors
  of the 2nd order Casimir operator on a list of polynomials
  of fixed weight and degree. The output is of the form 
     [[[evalue1,mult1,[evector11,....,evector1k]],[mbasis1,....,mbasisN]]
  where evalue1 is the first eigenvalue; mbasis1,...,mbasisN as a monomomial
  basis for the polynomials in plist, and evector11,...,evector1k are 
  arrays of N numbers corresponding to the components of the eigenvectors
  of the first eigenvalue with respect to the monomial basis mbasis1,...,
  mbasisN.

CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> LieTools[gSetup](A,2);Setting up Gtype = A   rnk = 2
> plist := LieTools[mkSgZeroWgts](2);

                                                2                 2
 plist := [g[1] g[8], g[2] g[7], g[3] g[6], g[4] , g[5] g[4], g[5] ]

> LieTools[DiagC2onSgPolys](plist);

  [[[8/3, 3, {

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

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

        [0, 1, {[3, 3, 3, 1, 1, 1]}]],

                                              2                 2
        [g[1] g[8], g[2] g[7], g[3] g[6], g[4] , g[5] g[4], g[5] ]]


SEE ALSO: 
