#### Green Polynomials for C2

####  W-rep key:
#  x[1] = [[], [1, 1]]   ,   orbit = [1, 1, 1, 1]  ,   A-rep = []    
#  x[2] = [[1, 1], []]   ,   orbit = [2, 1, 1]  ,   A-rep = []    
#  x[3] = [[1], [1]]   ,   orbit = [2, 2]    ,   A-rep = [1]   
#  x[4] = [[], [2]]    ,   orbit = [2, 2]    ,   A-rep = [-1]  
#  x[5] = [[2], []]    ,   orbit = [4]       ,   A-rep = []    


###   Green Polynomials by Orbit

orbit #1 : [1, 1, 1, 1]
  dim = 0
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 10*V[0]
  Z_G(x)_0 = C2

  # Green Polys by orbit reps
    #1.1 : x[1]  :  [1, 1, 1, 1],[]  : [[2], []]
        Qxi[C2,1,1] = (x[1])*q^4
                    + (x[3])*q^3
                    + (x[2]+x[4])*q^2
                    + (x[3])*q
                    + x[5]

  # Green Polys by conj class in A(O)
    #1.1  :  c = ()
        |O_x_c^F| = 1
        Qxc[C2,1,1] = (x[1])*q^4
                     + (x[3])*q^3
                     + (x[2]+x[4])*q^2
                     + (x[3])*q
                     + x[5]


orbit #2 : [2, 1, 1]
  dim = 4
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 2*V[1]+V[2]+3*V[0]
  Z_G(x)_0 = O1+Sp2

  # Green Polys by orbit reps
    #2.1 : x[2]  :  [2, 1, 1],[]  : [[1, 1], []]
        Qxi[C2,2,1] = (x[2])*q^2
                    + (x[3])*q
                    + x[5]

  # Green Polys by conj class in A(O)
    #2.1  :  c = ()
        |O_x_c^F| = q^4-1
        Qxc[C2,2,1] = (x[2])*q^2
                     + (x[3])*q
                     + x[5]


orbit #3 : [2, 2]
  dim = 6
  A(O) = Z2  ,  |A(O)_0| = 2
  g_s = 3*V[2]+V[0]
  Z_G(x)_0 = O2

  # Green Polys by orbit reps
    #3.1 : x[3]  :  [2, 2],[1]  : [[1], [1]]
        Qxi[C2,3,1] = (x[3])*q
                    + x[5]
    #3.2 : x[4]  :  [2, 2],[-1]  : [[], [2]]
        Qxi[C2,3,2] = (x[4])*q

  # Green Polys by conj class in A(O)
    #3.1  :  c = ()
        |O_x_c^F| = 1/2*q*(q+1)*(q^4-1)
        Qxc[C2,3,1] = (x[3]+x[4])*q
                     + x[5]
    #3.2  :  c = (1)
        |O_x_c^F| = 1/2*q*(q-1)*(q^4-1)
        Qxc[C2,3,2] = (x[3]-x[4])*q
                     + x[5]


orbit #4 : [4]
  dim = 8
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[6]+V[2]
  Z_G(x)_0 = O1

  # Green Polys by orbit reps
    #4.1 : x[5]  :  [4],[]  : [[2], []]
        Qxi[C2,4,1] = x[5]


  # Green Polys by conj class in A(O)
    #4.1  :  c = ()
        |O_x_c^F| = q^2*(q^2-1)*(q^4-1)
        Qxc[C2,4,1] = x[5]