FUNCTION: LieTools/SgProjectC2Eigenspace
USAGE: SgProject2C2EigenSpace(plist,hfw);
SYNOPSIS: SgProjectC2Eigenspace(plist,hfw) will produce a basis for 
  the kernel of C2 - C2[hfw] within the span of the polynomials
  in plist. Here C2[fhw] is the (properly normalized) eigenvalue of second
  order Casimir operator on an irreducible summand of S(g) of highest 
  weight fhw, specified in terms of a basis of fundamental weights.  
CAVEATS: requires a previously initialized global Lie algebra environment.
  (See LieTools[gSetup].)
EXAMPLE: 
> with(LieTools):
> gSetup(A,2):
Setting up Gtype = A   rnk = 2
> s2m := SgMkZeroWgtMonos(2);

              2      2
  s2m := {g[4] , g[5] , g[1] g[8], g[2] g[7], g[3] g[6], g[4] g[5]}

> SgProjectC2Eigenspace(s2m,[0,0]);

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

         + g[4] g[5]]

SEE ALSO: 
