FUNCTION: LieTools/ReduceChar
USAGE: ReduceChar(chi,Gt); ReduceChar(chi); ReduceChar(chi,Gtype,rnk);
SYNOPSIS: ReduceChar(chi,Gt) yields the reducible (finite-dimensional) representation of
  Gt with character chi. When called with a single argument chi, it is necessary to first
  initialize a global Lie algebra environment (see LieTools[gSetup]).
EXAMPLE: 
> x1 := 2*LieTools[Char]([1,0],G2) + LieTools[Char]([0,1],G2) + LieTools[Char]([1,1],G2);

  x1 := 7 X[1, 0] + 8 X[0, 0] + 2 X[2, 0] + 2 X[-2, 2] + 2 X[4, -2]

         + 2 X[-4, 2] + 2 X[2, -2] + 2 X[-2, 0] + 7 X[-1, 1]

         + 7 X[2, -1] + 7 X[-2, 1] + 7 X[1, -1] + 7 X[-1, 0]

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

         + 3 X[-3, 1] + 3 X[0, -1] + X[1, 1] + X[-1, 2] + X[4, -1]

         + X[5, -2] + X[-4, 3] + X[-5, 3] + X[5, -3] + X[4, -3]

         + X[-5, 2] + X[-4, 1] + X[1, -2] + X[-1, -1]

> LieTools[ReduceChar](x1,G2);

                   XX[1, 1] + XX[0, 1] + 2 XX[1, 0]


SEE ALSO: LieTools[Char]
