FUNCTION: LieTools/DecomposeChar
USAGE: DecomposeChar(x,Gt); DecomposeChar(x); DecomposeChar(x,Gtype,rnk)
SYNOPSIS: DecomposeChar(x,Gt) decomposes a character x into a sum of characters of
  of irreducible finite dimensional representations.
  If called with a single argument x, it is necessary that a global Lie algebra
  environment has been initialized (see LieTools[gSetup]).
EXAMPLE: 
> xc1 := LieTools[Char]([1,0],G2); xc2 := LieTools[Char]([0,1],G2);

  xc1 := X[1, 0] + X[-1, 1] + X[2, -1] + X[-2, 1] + X[1, -1]

         + X[-1, 0] + X[0, 0]


  xc2 := X[0, 1] + X[3, -1] + X[-3, 2] + X[3, -2] + X[-3, 1]

         + X[0, -1] + X[1, 0] + X[-1, 1] + X[2, -1] + X[-2, 1]

         + X[1, -1] + X[-1, 0] + 2 X[0, 0]

> xc := xc1 +xc2;

  xc := 2 X[1, 0] + 2 X[-1, 1] + 2 X[2, -1] + 2 X[-2, 1] + 2 X[1, -1]

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

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

> LieTools[DecomposeChar](xc,G2);

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


SEE ALSO: LieTools[Char], LieTools[Char2DomChar] 
