FUNCTION: LieTools/Char
USAGE: Char(hfw,Gt); Char(hfw); Char(hfw,Gtype,rnk)
SYNOPSIS: Char(hfw,Gt) will yield the character expansion 
  of the finite dimensional representation with highest weight fwgt. 
  We use Coxeter/Weyl's MultWeights to determine the
  multiplicities of the dominant weights inside the 
  representation and then a call to Coxeter/Weyl's Orbit
  to find the other weights in the representation with the
  same multiplicities. A typical term in Char(hfw,Gt) 
  is of the form m*X[op(w)] and corresponds to the existence of 
  a weight w (expressed in terms of a basis of fundamental weights)
  occuring in the f.d. representation of Gt with highest
  weight hfw with multiplicity m.
REMARK: One can call Char with a single argument hfw if the 
  global Lie algebra environment has been set up (via a call
  to LieTools[gSetup].  One can also compute the character
  of a representation of a semisimple Lie algebra Gt via
  a call like LieTools[Char](hfw,Gt), provided that the
  weight hfw is interpreted as the concatenation of the highest
  weights of the finite dimensional representations of the
  simple summands of Gt (arranged in the order given by
  Coxeter[CoxOrder]).  
EXAMPLES: 
> x := Char([0,1],G,2);

  x := 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]

> x := Char([1,0,1],A1*B2);
  x := X[1, 0, 1] + X[-1, 0, 1] + X[1, 1, -1] + X[-1, 1, -1]

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

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