#### Green Polynomials for C3

####  W-rep key:
#  x[1] = [[], [1, 1, 1]]   ,   orbit = [1, 1, 1, 1, 1, 1]  ,   A-rep = []    
#  x[2] = [[1, 1, 1], []]   ,   orbit = [2, 1, 1, 1, 1]  ,   A-rep = []    
#  x[3] = [[1], [1, 1]]   ,   orbit = [2, 2, 1, 1]  ,   A-rep = [1]   
#  x[4] = [[], [2, 1]]   ,   orbit = [2, 2, 1, 1]  ,   A-rep = [-1]  
#  x[5] = [[1, 1], [1]]   ,   orbit = [2, 2, 2]  ,   A-rep = []    
#  x[6] = [[1], [2]]   ,   orbit = [3, 3]    ,   A-rep = []    
#  x[7] = [[2, 1], []]   ,   orbit = [4, 1, 1]  ,   A-rep = []    
#  x[8] = [[2], [1]]   ,   orbit = [4, 2]    ,   A-rep = [1]   
#  x[9] = [[], [3]]    ,   orbit = [4, 2]    ,   A-rep = [-1]  
#  x[10] = [[3], []]    ,   orbit = [6]       ,   A-rep = []    


###   Green Polynomials by Orbit

orbit #1 : [1, 1, 1, 1, 1, 1]
  dim = 0
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 21*V[0]
  Z_G(x)_0 = C3

  # Green Polys by orbit reps
    #1.1 : x[1]  :  [1, 1, 1, 1, 1, 1],[]  : [[3], []]
        Qxi[C3,1,1] = (x[1])*q^9
                    + (x[3])*q^8
                    + (x[4]+x[5])*q^7
                    + (x[2]+x[3]+x[6])*q^6
                    + (x[4]+x[5]+x[8])*q^5
                    + (x[3]+x[6]+x[7])*q^4
                    + (x[5]+x[8]+x[9])*q^3
                    + (x[6]+x[7])*q^2
                    + (x[8])*q
                    + x[10]

  # Green Polys by conj class in A(O)
    #1.1  :  c = ()
        |O_x_c^F| = 1
        Qxc[C3,1,1] = (x[1])*q^9
                     + (x[3])*q^8
                     + (x[4]+x[5])*q^7
                     + (x[2]+x[3]+x[6])*q^6
                     + (x[4]+x[5]+x[8])*q^5
                     + (x[3]+x[6]+x[7])*q^4
                     + (x[5]+x[8]+x[9])*q^3
                     + (x[6]+x[7])*q^2
                     + (x[8])*q
                     + x[10]


orbit #2 : [2, 1, 1, 1, 1]
  dim = 6
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 4*V[1]+V[2]+10*V[0]
  Z_G(x)_0 = O1+Sp4

  # Green Polys by orbit reps
    #2.1 : x[2]  :  [2, 1, 1, 1, 1],[]  : [[1, 1, 1], []]
        Qxi[C3,2,1] = (x[2])*q^6
                    + (x[5])*q^5
                    + (x[3]+x[7])*q^4
                    + (x[5]+x[8])*q^3
                    + (x[6]+x[7])*q^2
                    + (x[8])*q
                    + x[10]

  # Green Polys by conj class in A(O)
    #2.1  :  c = ()
        |O_x_c^F| = q^6-1
        Qxc[C3,2,1] = (x[2])*q^6
                     + (x[5])*q^5
                     + (x[3]+x[7])*q^4
                     + (x[5]+x[8])*q^3
                     + (x[6]+x[7])*q^2
                     + (x[8])*q
                     + x[10]


orbit #3 : [2, 2, 1, 1]
  dim = 10
  A(O) = Z2  ,  |A(O)_0| = 2
  g_s = 4*V[1]+3*V[2]+4*V[0]
  Z_G(x)_0 = Sp2+O2

  # Green Polys by orbit reps
    #3.1 : x[3]  :  [2, 2, 1, 1],[1]  : [[1], [1, 1]]
        Qxi[C3,3,1] = (x[3])*q^4
                    + (x[5]+x[8])*q^3
                    + (x[6]+x[7])*q^2
                    + (x[8])*q
                    + x[10]
    #3.2 : x[4]  :  [2, 2, 1, 1],[-1]  : [[], [2, 1]]
        Qxi[C3,3,2] = (x[4])*q^4
                    + (x[6])*q^3
                    + (x[9])*q^2

  # Green Polys by conj class in A(O)
    #3.1  :  c = ()
        |O_x_c^F| = 1/2*q*(q+1)*(q^2+1)*(q^6-1)
        Qxc[C3,3,1] = (x[3]+x[4])*q^4
                     + (x[5]+x[6]+x[8])*q^3
                     + (x[6]+x[7]+x[9])*q^2
                     + (x[8])*q
                     + x[10]
    #3.2  :  c = (1)
        |O_x_c^F| = 1/2*q*(q-1)*(q^2+1)*(q^6-1)
        Qxc[C3,3,2] = (x[3]-x[4])*q^4
                     + (x[5]-x[6]+x[8])*q^3
                     + (x[6]+x[7]-x[9])*q^2
                     + (x[8])*q
                     + x[10]


orbit #4 : [2, 2, 2]
  dim = 12
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 6*V[2]+3*V[0]
  Z_G(x)_0 = O3

  # Green Polys by orbit reps
    #4.1 : x[5]  :  [2, 2, 2],[]  : [[1, 1], [1]]
        Qxi[C3,4,1] = (x[5])*q^3
                    + (x[6]+x[7])*q^2
                    + (x[8])*q
                    + x[10]

  # Green Polys by conj class in A(O)
    #4.1  :  c = ()
        |O_x_c^F| = q^2*(q^4-1)*(q^6-1)
        Qxc[C3,4,1] = (x[5])*q^3
                     + (x[6]+x[7])*q^2
                     + (x[8])*q
                     + x[10]


orbit #5 : [3, 3]
  dim = 14
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 3*V[4]+V[2]+3*V[0]
  Z_G(x)_0 = Sp2

  # Green Polys by orbit reps
    #5.1 : x[6]  :  [3, 3],[]  : [[1], [2]]
        Qxi[C3,5,1] = (x[6])*q^2
                    + (x[8]+x[9])*q
                    + x[10]

  # Green Polys by conj class in A(O)
    #5.1  :  c = ()
        |O_x_c^F| = q^4*(q^4-1)*(q^6-1)
        Qxc[C3,5,1] = (x[6])*q^2
                     + (x[8]+x[9])*q
                     + x[10]


orbit #6 : [4, 1, 1]
  dim = 14
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[6]+2*V[3]+V[2]+3*V[0]
  Z_G(x)_0 = O1+Sp2

  # Green Polys by orbit reps
    #6.1 : x[7]  :  [4, 1, 1],[]  : [[2, 1], []]
        Qxi[C3,6,1] = (x[7])*q^2
                    + (x[8])*q
                    + x[10]

  # Green Polys by conj class in A(O)
    #6.1  :  c = ()
        |O_x_c^F| = q^4*(q^4-1)*(q^6-1)
        Qxc[C3,6,1] = (x[7])*q^2
                     + (x[8])*q
                     + x[10]


orbit #7 : [4, 2]
  dim = 16
  A(O) = Z2  ,  |A(O)_0| = 2
  g_s = V[6]+V[4]+3*V[2]
  Z_G(x)_0 = 2*O1

  # Green Polys by orbit reps
    #7.1 : x[8]  :  [4, 2],[1]  : [[2], [1]]
        Qxi[C3,7,1] = (x[8])*q
                    + x[10]
    #7.2 : x[9]  :  [4, 2],[-1]  : [[], [3]]
        Qxi[C3,7,2] = (x[9])*q

  # Green Polys by conj class in A(O)
    #7.1  :  c = ()
        |O_x_c^F| = 1/2*q^4*(q^2-1)*(q^4-1)*(q^6-1)
        Qxc[C3,7,1] = (x[8]+x[9])*q
                     + x[10]
    #7.2  :  c = (1)
        |O_x_c^F| = 1/2*q^4*(q^2-1)*(q^4-1)*(q^6-1)
        Qxc[C3,7,2] = (x[8]-x[9])*q
                     + x[10]


orbit #8 : [6]
  dim = 18
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[10]+V[6]+V[2]
  Z_G(x)_0 = O1

  # Green Polys by orbit reps
    #8.1 : x[10]  :  [6],[]  : [[3], []]
        Qxi[C3,8,1] = x[10]


  # Green Polys by conj class in A(O)
    #8.1  :  c = ()
        |O_x_c^F| = q^6*(q^2-1)*(q^4-1)*(q^6-1)
        Qxc[C3,8,1] = x[10]