#### Green Polynomials for A2

####  W-rep key:
#  x[1] = [1, 1, 1]    ,   orbit = [1, 1, 1]  ,   A-rep = []    
#  x[2] = [2, 1]       ,   orbit = [2, 1]    ,   A-rep = []    
#  x[3] = [3]          ,   orbit = [3]       ,   A-rep = []    


###   Green Polynomials by Orbit

orbit #1 : [1, 1, 1]
  dim = 0
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 8*V[0]
  Z_G(x)_0 = A2

  # Green Polys by orbit reps
    #1.1 : x[1]  :  [1, 1, 1],[]  : [3]     
        Qxi[A2,1,1] = (x[1])*q^3
                    + (x[2])*q^2
                    + (x[2])*q
                    + x[3]

  # Green Polys by conj class in A(O)
    #1.1  :  c = ()
        |O_x_c^F| = 1
        Qxc[A2,1,1] = (x[1])*q^3
                     + (x[2])*q^2
                     + (x[2])*q
                     + x[3]


orbit #2 : [2, 1]
  dim = 4
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 2*V[1]+V[2]+V[0]
  Z_G(x)_0 = 2*GL1

  # Green Polys by orbit reps
    #2.1 : x[2]  :  [2, 1],[]  : [2, 1]  
        Qxi[A2,2,1] = (x[2])*q
                    + x[3]

  # Green Polys by conj class in A(O)
    #2.1  :  c = ()
        |O_x_c^F| = (q+1)*(q^3-1)
        Qxc[A2,2,1] = (x[2])*q
                     + x[3]


orbit #3 : [3]
  dim = 6
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[4]+V[2]
  Z_G(x)_0 = GL1

  # Green Polys by orbit reps
    #3.1 : x[3]  :  [3],[]  : [3]     
        Qxi[A2,3,1] = x[3]


  # Green Polys by conj class in A(O)
    #3.1  :  c = ()
        |O_x_c^F| = q*(q^2-1)*(q^3-1)
        Qxc[A2,3,1] = x[3]