#### Green Polynomials for G2

####  W-rep key:
#  x[1] = phi[1,6]     ,   orbit = 0         ,   A-rep = [1]   
#  x[2] = phi[1,3,2]   ,   orbit = A1        ,   A-rep = [1]   
#  x[3] = phi[2,2]     ,   orbit = A1s       ,   A-rep = [1]   
#  x[4] = phi[2,1]     ,   orbit = G2(a1)    ,   A-rep = [3]   
#  x[5] = phi[1,3,1]   ,   orbit = G2(a1)    ,   A-rep = [2, 1]
#  x[6] = phi[1,0]     ,   orbit = G2        ,   A-rep = [1]   


###   Green Polynomials by Orbit

orbit #1 : 0
  dim = 0
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 14*V[0]
  Z_G(x)_0 = G2

  # Green Polys by orbit reps
    #1.1 : x[1]  :  0,[1]  : phi[1,6]
        Qxi[G2,1,1] = (x[1])*q^6
                    + (x[4])*q^5
                    + (x[3])*q^4
                    + (x[2]+x[5])*q^3
                    + (x[3])*q^2
                    + (x[4])*q
                    + x[6]

  # Green Polys by conj class in A(O)
    #1.1  :  c = ()
        |O_x_c^F| = 1
        Qxc[G2,1,1] = (x[1])*q^6
                     + (x[4])*q^5
                     + (x[3])*q^4
                     + (x[2]+x[5])*q^3
                     + (x[3])*q^2
                     + (x[4])*q
                     + x[6]


orbit #2 : A1
  dim = 6
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 4*V[1]+V[2]+3*V[0]
  Z_G(x)_0 = A1

  # Green Polys by orbit reps
    #2.1 : x[2]  :  A1,[1]  : phi[1,3,2]
        Qxi[G2,2,1] = (x[2])*q^3
                    + (x[3])*q^2
                    + (x[4])*q
                    + x[6]

  # Green Polys by conj class in A(O)
    #2.1  :  c = ()
        |O_x_c^F| = q^6-1
        Qxc[G2,2,1] = (x[2])*q^3
                     + (x[3])*q^2
                     + (x[4])*q
                     + x[6]


orbit #3 : A1s
  dim = 8
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[2]+2*V[3]+3*V[0]
  Z_G(x)_0 = A1

  # Green Polys by orbit reps
    #3.1 : x[3]  :  A1s,[1]  : phi[2,2]
        Qxi[G2,3,1] = (x[3])*q^2
                    + (x[4]+x[5])*q
                    + x[6]

  # Green Polys by conj class in A(O)
    #3.1  :  c = ()
        |O_x_c^F| = q^2*(q^6-1)
        Qxc[G2,3,1] = (x[3])*q^2
                     + (x[4]+x[5])*q
                     + x[6]


orbit #4 : G2(a1)
  dim = 10
  A(O) = S3  ,  |A(O)_0| = 2
  g_s = V[4]+3*V[2]
  Z_G(x)_0 = 0

  # Green Polys by orbit reps
    #4.1 : x[4]  :  G2(a1),[3]  : phi[2,1]
        Qxi[G2,4,1] = (x[4])*q
                    + x[6]
    #4.2 : x[5]  :  G2(a1),[2, 1]  : phi[1,3,1]
        Qxi[G2,4,2] = (x[5])*q

  # Green Polys by conj class in A(O)
    #4.1  :  c = ()
        |O_x_c^F| = 1/6*q^2*(q^2-1)*(q^6-1)
        Qxc[G2,4,1] = (x[4]+2*x[5])*q
                     + x[6]
    #4.2  :  c = (1)
        |O_x_c^F| = 1/2*q^2*(q^2-1)*(q^6-1)
        Qxc[G2,4,2] = (x[4])*q
                     + x[6]
    #4.3  :  c = (12)
        |O_x_c^F| = 1/3*q^2*(q^2-1)*(q^6-1)
        Qxc[G2,4,3] = (x[4]-x[5])*q
                     + x[6]


orbit #5 : G2
  dim = 12
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[10]+V[2]
  Z_G(x)_0 = 0

  # Green Polys by orbit reps
    #5.1 : x[6]  :  G2,[1]  : phi[1,0]
        Qxi[G2,5,1] = x[6]


  # Green Polys by conj class in A(O)
    #5.1  :  c = ()
        |O_x_c^F| = q^4*(q^2-1)*(q^6-1)
        Qxc[G2,5,1] = x[6]