#### Green Polynomials for A4

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


###   Green Polynomials by Orbit

orbit #1 : [1, 1, 1, 1, 1]
  dim = 0
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 24*V[0]
  Z_G(x)_0 = A4

  # Green Polys by orbit reps
    #1.1 : x[1]  :  [1, 1, 1, 1, 1],[]  : [5]     
        Qxi[A4,1,1] = (x[1])*q^10
                    + (x[2])*q^9
                    + (x[2]+x[3])*q^8
                    + (x[2]+x[3]+x[4])*q^7
                    + (x[2]+x[3]+x[4]+x[5])*q^6
                    + (x[3]+2*x[4]+x[5])*q^5
                    + (x[3]+x[4]+x[5]+x[6])*q^4
                    + (x[4]+x[5]+x[6])*q^3
                    + (x[5]+x[6])*q^2
                    + (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #1.1  :  c = ()
        |O_x_c^F| = 1
        Qxc[A4,1,1] = (x[1])*q^10
                     + (x[2])*q^9
                     + (x[2]+x[3])*q^8
                     + (x[2]+x[3]+x[4])*q^7
                     + (x[2]+x[3]+x[4]+x[5])*q^6
                     + (x[3]+2*x[4]+x[5])*q^5
                     + (x[3]+x[4]+x[5]+x[6])*q^4
                     + (x[4]+x[5]+x[6])*q^3
                     + (x[5]+x[6])*q^2
                     + (x[6])*q
                     + x[7]


orbit #2 : [2, 1, 1, 1]
  dim = 8
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 6*V[1]+V[2]+9*V[0]
  Z_G(x)_0 = GL3+GL1

  # Green Polys by orbit reps
    #2.1 : x[2]  :  [2, 1, 1, 1],[]  : [2, 1, 1, 1]
        Qxi[A4,2,1] = (x[2])*q^6
                    + (x[3]+x[4])*q^5
                    + (x[3]+x[4]+x[5])*q^4
                    + (x[4]+x[5]+x[6])*q^3
                    + (x[5]+x[6])*q^2
                    + (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #2.1  :  c = ()
        |O_x_c^F| = (q+1)*(q^2+1)*(q^5-1)
        Qxc[A4,2,1] = (x[2])*q^6
                     + (x[3]+x[4])*q^5
                     + (x[3]+x[4]+x[5])*q^4
                     + (x[4]+x[5]+x[6])*q^3
                     + (x[5]+x[6])*q^2
                     + (x[6])*q
                     + x[7]


orbit #3 : [2, 2, 1]
  dim = 12
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = 4*V[2]+4*V[1]+4*V[0]
  Z_G(x)_0 = GL2+GL1

  # Green Polys by orbit reps
    #3.1 : x[3]  :  [2, 2, 1],[]  : [2, 2, 1]
        Qxi[A4,3,1] = (x[3])*q^4
                    + (x[4]+x[5])*q^3
                    + (x[5]+x[6])*q^2
                    + (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #3.1  :  c = ()
        |O_x_c^F| = q*(q^2+q+1)*(q^4-1)*(q^5-1)
        Qxc[A4,3,1] = (x[3])*q^4
                     + (x[4]+x[5])*q^3
                     + (x[5]+x[6])*q^2
                     + (x[6])*q
                     + x[7]


orbit #4 : [3, 1, 1]
  dim = 14
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[4]+5*V[2]+4*V[0]
  Z_G(x)_0 = GL2+GL1

  # Green Polys by orbit reps
    #4.1 : x[4]  :  [3, 1, 1],[]  : [3, 1, 1]
        Qxi[A4,4,1] = (x[4])*q^3
                    + (x[5]+x[6])*q^2
                    + (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #4.1  :  c = ()
        |O_x_c^F| = q^3*(q^2+q+1)*(q^4-1)*(q^5-1)
        Qxc[A4,4,1] = (x[4])*q^3
                     + (x[5]+x[6])*q^2
                     + (x[6])*q
                     + x[7]


orbit #5 : [3, 2]
  dim = 16
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[4]+2*V[3]+2*V[2]+2*V[1]+V[0]
  Z_G(x)_0 = 2*GL1

  # Green Polys by orbit reps
    #5.1 : x[5]  :  [3, 2],[]  : [3, 2]  
        Qxi[A4,5,1] = (x[5])*q^2
                    + (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #5.1  :  c = ()
        |O_x_c^F| = q^3*(q+1)*(q^3-1)*(q^4-1)*(q^5-1)
        Qxc[A4,5,1] = (x[5])*q^2
                     + (x[6])*q
                     + x[7]


orbit #6 : [4, 1]
  dim = 18
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[6]+V[4]+2*V[3]+V[2]+V[0]
  Z_G(x)_0 = 2*GL1

  # Green Polys by orbit reps
    #6.1 : x[6]  :  [4, 1],[]  : [4, 1]  
        Qxi[A4,6,1] = (x[6])*q
                    + x[7]

  # Green Polys by conj class in A(O)
    #6.1  :  c = ()
        |O_x_c^F| = q^5*(q+1)*(q^3-1)*(q^4-1)*(q^5-1)
        Qxc[A4,6,1] = (x[6])*q
                     + x[7]


orbit #7 : [5]
  dim = 20
  A(O) = 1  ,  |A(O)_0| = 1
  g_s = V[8]+V[6]+V[4]+V[2]
  Z_G(x)_0 = GL1

  # Green Polys by orbit reps
    #7.1 : x[7]  :  [5],[]  : [5]     
        Qxi[A4,7,1] = x[7]


  # Green Polys by conj class in A(O)
    #7.1  :  c = ()
        |O_x_c^F| = q^6*(q^2-1)*(q^3-1)*(q^4-1)*(q^5-1)
        Qxc[A4,7,1] = x[7]