#### Green Polynomials for F4 #### W-rep key: # x[1] = phi[1,24] , orbit = 0 , A-rep = [1] # x[2] = phi[2,16,2] , orbit = A1 , A-rep = [1] # x[3] = phi[4,13] , orbit = A1s , A-rep = [2] # x[4] = phi[2,16,1] , orbit = A1s , A-rep = [1, 1] # x[5] = phi[9,10] , orbit = A1+A1s , A-rep = [1] # x[6] = phi[8,9,2] , orbit = A2 , A-rep = [2] # x[7] = phi[1,12,2] , orbit = A2 , A-rep = [1, 1] # x[8] = phi[8,9,1] , orbit = A2s , A-rep = [1] # x[9] = phi[4,7,2] , orbit = A2+A1s , A-rep = [1] # x[10] = phi[9,6,2] , orbit = B2 , A-rep = [2] # x[11] = phi[4,8] , orbit = B2 , A-rep = [1, 1] # x[12] = phi[6,6,1] , orbit = A2s+A1 , A-rep = [1] # x[13] = phi[16,5] , orbit = C3(a1) , A-rep = [2] # x[14] = phi[4,7,1] , orbit = C3(a1) , A-rep = [1, 1] # x[15] = phi[12,4] , orbit = F4(a3) , A-rep = [4] # x[16] = phi[9,6,1] , orbit = F4(a3) , A-rep = [3, 1] # x[17] = phi[6,6,2] , orbit = F4(a3) , A-rep = [2, 2] # x[18] = phi[1,12,1] , orbit = F4(a3) , A-rep = [2, 1, 1] # x[19] = phi[8,3,2] , orbit = B3 , A-rep = [1] # x[20] = phi[8,3,1] , orbit = C3 , A-rep = [1] # x[21] = phi[9,2] , orbit = F4(a2) , A-rep = [2] # x[22] = phi[2,4,2] , orbit = F4(a2) , A-rep = [1, 1] # x[23] = phi[4,1] , orbit = F4(a1) , A-rep = [2] # x[24] = phi[2,4,1] , orbit = F4(a1) , A-rep = [1, 1] # x[25] = phi[1,0] , orbit = F4 , A-rep = [1] ### Green Polynomials by Orbit orbit #1 : 0 dim = 0 A(O) = 1 , |A(O)_0| = 1 g_s = 52*V[0] Z_G(x)_0 = F4 # Green Polys by orbit reps #1.1 : x[1] : 0,[1] : phi[1,24] Qxi[F4,1,1] = (x[1])*q^24 + (x[3])*q^23 + (x[5])*q^22 + (x[6]+x[8])*q^21 + (x[2]+x[4]+x[5]+x[15])*q^20 + (x[3]+x[6]+x[8]+x[13])*q^19 + (2*x[5]+x[10]+x[12]+x[16]+x[17])*q^18 + (x[3]+x[6]+x[8]+x[9]+2*x[13]+x[14])*q^17 + (x[2]+x[4]+x[5]+x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17])*q^16 + (2*x[6]+2*x[8]+2*x[13]+x[19]+x[20])*q^15 + (2*x[5]+2*x[10]+2*x[15]+2*x[16]+x[21])*q^14 + (x[3]+x[6]+x[8]+x[9]+3*x[13]+x[14]+x[19]+x[20])*q^13 + (x[5]+x[7]+x[10]+2*x[11]+2*x[12]+2*x[15]+x[16]+2*x[17]+x[18]+x[21])*q^12 + (x[6]+x[8]+x[9]+3*x[13]+x[14]+x[19]+x[20]+x[23])*q^11 + (x[5]+2*x[10]+2*x[15]+2*x[16]+2*x[21])*q^10 + (x[6]+x[8]+2*x[13]+2*x[19]+2*x[20])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17]+x[21]+x[22]+x[24])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #1.1 : c = () |O_x_c^F| = 1 Qxc[F4,1,1] = (x[1])*q^24 + (x[3])*q^23 + (x[5])*q^22 + (x[6]+x[8])*q^21 + (x[2]+x[4]+x[5]+x[15])*q^20 + (x[3]+x[6]+x[8]+x[13])*q^19 + (2*x[5]+x[10]+x[12]+x[16]+x[17])*q^18 + (x[3]+x[6]+x[8]+x[9]+2*x[13]+x[14])*q^17 + (x[2]+x[4]+x[5]+x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17])*q^16 + (2*x[6]+2*x[8]+2*x[13]+x[19]+x[20])*q^15 + (2*x[5]+2*x[10]+2*x[15]+2*x[16]+x[21])*q^14 + (x[3]+x[6]+x[8]+x[9]+3*x[13]+x[14]+x[19]+x[20])*q^13 + (x[5]+x[7]+x[10]+2*x[11]+2*x[12]+2*x[15]+x[16]+2*x[17]+x[18]+x[21])*q^12 + (x[6]+x[8]+x[9]+3*x[13]+x[14]+x[19]+x[20]+x[23])*q^11 + (x[5]+2*x[10]+2*x[15]+2*x[16]+2*x[21])*q^10 + (x[6]+x[8]+2*x[13]+2*x[19]+2*x[20])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17]+x[21]+x[22]+x[24])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #2 : A1 dim = 16 A(O) = 1 , |A(O)_0| = 1 g_s = 14*V[1]+V[2]+21*V[0] Z_G(x)_0 = C3 # Green Polys by orbit reps #2.1 : x[2] : A1,[1] : phi[2,16,2] Qxi[F4,2,1] = (x[2])*q^16 + (x[6])*q^15 + (x[5]+x[10])*q^14 + (x[3]+x[6]+x[9]+x[13])*q^13 + (x[5]+x[7]+x[10]+x[11]+x[12]+x[15]+x[17])*q^12 + (x[6]+x[8]+x[9]+2*x[13]+x[19])*q^11 + (x[5]+2*x[10]+2*x[15]+x[16]+x[21])*q^10 + (x[6]+x[8]+2*x[13]+2*x[19]+x[20])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17]+x[21]+x[22])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #2.1 : c = () |O_x_c^F| = (q^4+1)*(q^12-1) Qxc[F4,2,1] = (x[2])*q^16 + (x[6])*q^15 + (x[5]+x[10])*q^14 + (x[3]+x[6]+x[9]+x[13])*q^13 + (x[5]+x[7]+x[10]+x[11]+x[12]+x[15]+x[17])*q^12 + (x[6]+x[8]+x[9]+2*x[13]+x[19])*q^11 + (x[5]+2*x[10]+2*x[15]+x[16]+x[21])*q^10 + (x[6]+x[8]+2*x[13]+2*x[19]+x[20])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17]+x[21]+x[22])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #3 : A1s dim = 22 A(O) = S2 , |A(O)_0| = 2 g_s = 8*V[1]+7*V[2]+15*V[0] Z_G(x)_0 = A3 # Green Polys by orbit reps #3.1 : x[3] : A1s,[2] : phi[4,13] Qxi[F4,3,1] = (x[3])*q^13 + (x[5]+x[17])*q^12 + (x[6]+x[8]+x[13])*q^11 + (x[5]+x[10]+2*x[15]+x[16])*q^10 + (x[6]+x[8]+2*x[13]+x[19]+x[20])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16]+x[17]+x[21])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #3.2 : x[4] : A1s,[1, 1] : phi[2,16,1] Qxi[F4,3,2] = (x[4])*q^13 + (x[8])*q^12 + (x[5]+x[16])*q^11 + (x[8]+x[13]+x[14])*q^10 + (x[11]+x[12]+x[15]+x[16]+x[18])*q^9 + (x[13]+x[14]+x[20])*q^8 + (x[16]+x[21])*q^7 + (x[20])*q^6 + (x[24])*q^5 # Green Polys by conj class in A(O) #3.1 : c = () |O_x_c^F| = 1/2*q^3*(q^3+1)*(q^4+1)*(q^12-1) Qxc[F4,3,1] = (x[3]+x[4])*q^13 + (x[5]+x[8]+x[17])*q^12 + (x[5]+x[6]+x[8]+x[13]+x[16])*q^11 + (x[5]+x[8]+x[10]+x[13]+x[14]+2*x[15]+x[16])*q^10 + (x[6]+x[8]+x[11]+x[12]+2*x[13]+x[15]+x[16]+x[18]+x[19]+x[20])*q^9 + (x[10]+x[11]+x[12]+x[13]+x[14]+2*x[15]+x[16]+x[17]+x[20]+x[21])*q^8 + (x[9]+2*x[13]+x[14]+x[16]+x[19]+x[20]+x[21]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]+x[20]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23]+x[24])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #3.2 : c = (1) |O_x_c^F| = 1/2*q^3*(q^3-1)*(q^4+1)*(q^12-1) Qxc[F4,3,2] = (x[3]-x[4])*q^13 + (x[5]-x[8]+x[17])*q^12 + (-x[5]+x[6]+x[8]+x[13]-x[16])*q^11 + (x[5]-x[8]+x[10]-x[13]-x[14]+2*x[15]+x[16])*q^10 + (x[6]+x[8]-x[11]-x[12]+2*x[13]-x[15]-x[16]-x[18]+x[19]+x[20])*q^9 + (x[10]+x[11]+x[12]-x[13]-x[14]+2*x[15]+x[16]+x[17]-x[20]+x[21])*q^8 + (x[9]+2*x[13]+x[14]-x[16]+x[19]+x[20]-x[21]+x[23])*q^7 + (x[10]+x[12]+x[16]+x[17]-x[20]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23]-x[24])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #4 : A1+A1s dim = 28 A(O) = 1 , |A(O)_0| = 1 g_s = 2*V[3]+6*V[2]+10*V[1]+6*V[0] Z_G(x)_0 = 2*A1 # Green Polys by orbit reps #4.1 : x[5] : A1+A1s,[1] : phi[9,10] Qxi[F4,4,1] = (x[5])*q^10 + (x[6]+x[8]+x[13])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #4.1 : c = () |O_x_c^F| = q^4*(q^2+q+1)*(q^2-q+1)*(q^8-1)*(q^12-1) Qxc[F4,4,1] = (x[5])*q^10 + (x[6]+x[8]+x[13])*q^9 + (x[10]+x[11]+x[12]+2*x[15]+x[16])*q^8 + (x[9]+2*x[13]+x[14]+x[19]+x[20])*q^7 + (x[10]+x[12]+x[16]+x[17]+2*x[21])*q^6 + (x[13]+x[19]+x[20]+x[23])*q^5 + (x[15]+x[21]+x[22]+x[24])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #5 : A2 dim = 30 A(O) = S2 , |A(O)_0| = 2 g_s = V[4]+13*V[2]+8*V[0] Z_G(x)_0 = A2 # Green Polys by orbit reps #5.1 : x[6] : A2,[2] : phi[8,9,2] Qxi[F4,5,1] = (x[6])*q^9 + (x[10]+x[15])*q^8 + (x[9]+x[13]+x[19])*q^7 + (x[10]+x[12]+x[17]+x[21])*q^6 + (x[13]+x[19]+x[23])*q^5 + (x[15]+x[21]+x[22])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #5.2 : x[7] : A2,[1, 1] : phi[1,12,2] Qxi[F4,5,2] = (x[7])*q^9 + (x[9])*q^8 + (x[10])*q^7 + (x[19])*q^6 + (x[22])*q^5 # Green Polys by conj class in A(O) #5.1 : c = () |O_x_c^F| = 1/2*q^7*(q^3+1)*(q^8-1)*(q^12-1) Qxc[F4,5,1] = (x[6]+x[7])*q^9 + (x[9]+x[10]+x[15])*q^8 + (x[9]+x[10]+x[13]+x[19])*q^7 + (x[10]+x[12]+x[17]+x[19]+x[21])*q^6 + (x[13]+x[19]+x[22]+x[23])*q^5 + (x[15]+x[21]+x[22])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #5.2 : c = (1) |O_x_c^F| = 1/2*q^7*(q^3-1)*(q^8-1)*(q^12-1) Qxc[F4,5,2] = (x[6]-x[7])*q^9 + (-x[9]+x[10]+x[15])*q^8 + (x[9]-x[10]+x[13]+x[19])*q^7 + (x[10]+x[12]+x[17]-x[19]+x[21])*q^6 + (x[13]+x[19]-x[22]+x[23])*q^5 + (x[15]+x[21]+x[22])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #6 : A2s dim = 30 A(O) = 1 , |A(O)_0| = 1 g_s = 7*V[4]+V[2]+14*V[0] Z_G(x)_0 = G2 # Green Polys by orbit reps #6.1 : x[8] : A2s,[1] : phi[8,9,1] Qxi[F4,6,1] = (x[8])*q^9 + (x[15]+x[16])*q^8 + (x[13]+x[14]+x[20])*q^7 + (x[12]+x[16]+x[17]+x[18]+x[21])*q^6 + (x[13]+x[14]+x[20]+x[23])*q^5 + (x[15]+x[16]+x[21]+x[24])*q^4 + (x[19]+2*x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #6.1 : c = () |O_x_c^F| = q^10*(q^8-1)*(q^12-1) Qxc[F4,6,1] = (x[8])*q^9 + (x[15]+x[16])*q^8 + (x[13]+x[14]+x[20])*q^7 + (x[12]+x[16]+x[17]+x[18]+x[21])*q^6 + (x[13]+x[14]+x[20]+x[23])*q^5 + (x[15]+x[16]+x[21]+x[24])*q^4 + (x[19]+2*x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] orbit #7 : A2+A1s dim = 34 A(O) = 1 , |A(O)_0| = 1 g_s = 3*V[4]+2*V[3]+6*V[2]+4*V[1]+3*V[0] Z_G(x)_0 = A1 # Green Polys by orbit reps #7.1 : x[9] : A2+A1s,[1] : phi[4,7,2] Qxi[F4,7,1] = (x[9])*q^7 + (x[10]+x[12])*q^6 + (x[13]+x[19])*q^5 + (x[15]+x[21]+x[22])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #7.1 : c = () |O_x_c^F| = q^8*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,7,1] = (x[9])*q^7 + (x[10]+x[12])*q^6 + (x[13]+x[19])*q^5 + (x[15]+x[21]+x[22])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #8 : B2 dim = 36 A(O) = S2 , |A(O)_0| = 2 g_s = V[6]+4*V[4]+4*V[3]+V[2]+6*V[0] Z_G(x)_0 = 2*A1 # Green Polys by orbit reps #8.1 : x[10] : B2,[2] : phi[9,6,2] Qxi[F4,8,1] = (x[10])*q^6 + (x[13]+x[19])*q^5 + (x[15]+x[17]+x[21]+x[22])*q^4 + (x[19]+x[20]+x[23])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #8.2 : x[11] : B2,[1, 1] : phi[4,8] Qxi[F4,8,2] = (x[11])*q^6 + (x[13])*q^5 + (x[16]+x[21])*q^4 + (x[20])*q^3 + (x[24])*q^2 # Green Polys by conj class in A(O) #8.1 : c = () |O_x_c^F| = 1/2*q^12*(q^2-q+1)*(q^2+q+1)*(q^8-1)*(q^12-1) Qxc[F4,8,1] = (x[10]+x[11])*q^6 + (2*x[13]+x[19])*q^5 + (x[15]+x[16]+x[17]+2*x[21]+x[22])*q^4 + (x[19]+2*x[20]+x[23])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] #8.2 : c = (1) |O_x_c^F| = 1/2*q^12*(q^2-1)*(q^4+1)*(q^6-1)*(q^12-1) Qxc[F4,8,2] = (x[10]-x[11])*q^6 + (x[19])*q^5 + (x[15]-x[16]+x[17]+x[22])*q^4 + (x[19]+x[23])*q^3 + (x[21]-x[24])*q^2 + (x[23])*q + x[25] orbit #9 : A2s+A1 dim = 36 A(O) = 1 , |A(O)_0| = 1 g_s = 2*V[5]+3*V[4]+2*V[3]+2*V[2]+4*V[1]+3*V[0] Z_G(x)_0 = A1 # Green Polys by orbit reps #9.1 : x[12] : A2s+A1,[1] : phi[6,6,1] Qxi[F4,9,1] = (x[12])*q^6 + (x[13]+x[14])*q^5 + (x[15]+x[16]+x[21])*q^4 + (x[19]+2*x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #9.1 : c = () |O_x_c^F| = q^10*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,9,1] = (x[12])*q^6 + (x[13]+x[14])*q^5 + (x[15]+x[16]+x[21])*q^4 + (x[19]+2*x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] orbit #10 : C3(a1) dim = 38 A(O) = S2 , |A(O)_0| = 2 g_s = V[6]+2*V[5]+V[4]+4*V[3]+3*V[2]+3*V[0] Z_G(x)_0 = A1 # Green Polys by orbit reps #10.1 : x[13] : C3(a1),[2] : phi[16,5] Qxi[F4,10,1] = (x[13])*q^5 + (x[15]+x[16]+x[17]+x[21])*q^4 + (x[19]+2*x[20]+x[23])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] #10.2 : x[14] : C3(a1),[1, 1] : phi[4,7,1] Qxi[F4,10,2] = (x[14])*q^5 + (x[16]+x[18])*q^4 + (x[20])*q^3 + (x[24])*q^2 # Green Polys by conj class in A(O) #10.1 : c = () |O_x_c^F| = 1/2*q^12*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,10,1] = (x[13]+x[14])*q^5 + (x[15]+2*x[16]+x[17]+x[18]+x[21])*q^4 + (x[19]+3*x[20]+x[23])*q^3 + (x[21]+2*x[24])*q^2 + (x[23])*q + x[25] #10.2 : c = (1) |O_x_c^F| = 1/2*q^12*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,10,2] = (x[13]-x[14])*q^5 + (x[15]+x[17]-x[18]+x[21])*q^4 + (x[19]+x[20]+x[23])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] orbit #11 : F4(a3) dim = 40 A(O) = S4 , |A(O)_0| = 4 g_s = 2*V[6]+4*V[4]+6*V[2] Z_G(x)_0 = 0 # Green Polys by orbit reps #11.1 : x[15] : F4(a3),[4] : phi[12,4] Qxi[F4,11,1] = (x[15])*q^4 + (x[19]+x[20])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #11.2 : x[16] : F4(a3),[3, 1] : phi[9,6,1] Qxi[F4,11,2] = (x[16])*q^4 + (x[20])*q^3 + (x[24])*q^2 #11.3 : x[17] : F4(a3),[2, 2] : phi[6,6,2] Qxi[F4,11,3] = (x[17])*q^4 + (x[23])*q^3 #11.4 : x[18] : F4(a3),[2, 1, 1] : phi[1,12,1] Qxi[F4,11,4] = (x[18])*q^4 # Green Polys by conj class in A(O) #11.1 : c = () |O_x_c^F| = 1/24*q^12*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,11,1] = (x[15]+3*x[16]+2*x[17]+3*x[18])*q^4 + (x[19]+4*x[20]+2*x[23])*q^3 + (x[21]+3*x[24])*q^2 + (x[23])*q + x[25] #11.2 : c = (1) |O_x_c^F| = 1/4*q^12*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,11,2] = (x[15]+x[16]-x[18])*q^4 + (x[19]+2*x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] #11.3 : c = (13) |O_x_c^F| = 1/8*q^12*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,11,3] = (x[15]-x[16]+2*x[17]-x[18])*q^4 + (x[19]+2*x[23])*q^3 + (x[21]-x[24])*q^2 + (x[23])*q + x[25] #11.4 : c = (12) |O_x_c^F| = 1/3*q^12*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,11,4] = (x[15]-x[17])*q^4 + (x[19]+x[20]-x[23])*q^3 + (x[21])*q^2 + (x[23])*q + x[25] #11.5 : c = (123) |O_x_c^F| = 1/4*q^12*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,11,5] = (x[15]-x[16]+x[18])*q^4 + (x[19])*q^3 + (x[21]-x[24])*q^2 + (x[23])*q + x[25] orbit #12 : B3 dim = 42 A(O) = 1 , |A(O)_0| = 1 g_s = V[10]+5*V[6]+V[2]+3*V[0] Z_G(x)_0 = A1 # Green Polys by orbit reps #12.1 : x[19] : B3,[1] : phi[8,3,2] Qxi[F4,12,1] = (x[19])*q^3 + (x[21]+x[22])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #12.1 : c = () |O_x_c^F| = q^16*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,12,1] = (x[19])*q^3 + (x[21]+x[22])*q^2 + (x[23])*q + x[25] orbit #13 : C3 dim = 42 A(O) = 1 , |A(O)_0| = 1 g_s = V[10]+2*V[9]+V[6]+2*V[3]+V[2]+3*V[0] Z_G(x)_0 = A1 # Green Polys by orbit reps #13.1 : x[20] : C3,[1] : phi[8,3,1] Qxi[F4,13,1] = (x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] # Green Polys by conj class in A(O) #13.1 : c = () |O_x_c^F| = q^16*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,13,1] = (x[20])*q^3 + (x[21]+x[24])*q^2 + (x[23])*q + x[25] orbit #14 : F4(a2) dim = 44 A(O) = S2 , |A(O)_0| = 2 g_s = 2*V[10]+V[8]+V[6]+V[4]+3*V[2] Z_G(x)_0 = 0 # Green Polys by orbit reps #14.1 : x[21] : F4(a2),[2] : phi[9,2] Qxi[F4,14,1] = (x[21])*q^2 + (x[23])*q + x[25] #14.2 : x[22] : F4(a2),[1, 1] : phi[2,4,2] Qxi[F4,14,2] = (x[22])*q^2 # Green Polys by conj class in A(O) #14.1 : c = () |O_x_c^F| = 1/2*q^16*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,14,1] = (x[21]+x[22])*q^2 + (x[23])*q + x[25] #14.2 : c = (1) |O_x_c^F| = 1/2*q^16*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,14,2] = (x[21]-x[22])*q^2 + (x[23])*q + x[25] orbit #15 : F4(a1) dim = 46 A(O) = S2 , |A(O)_0| = 2 g_s = V[14]+2*V[10]+V[6]+V[4]+V[2] Z_G(x)_0 = 0 # Green Polys by orbit reps #15.1 : x[23] : F4(a1),[2] : phi[4,1] Qxi[F4,15,1] = (x[23])*q + x[25] #15.2 : x[24] : F4(a1),[1, 1] : phi[2,4,1] Qxi[F4,15,2] = (x[24])*q # Green Polys by conj class in A(O) #15.1 : c = () |O_x_c^F| = 1/2*q^18*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,15,1] = (x[23]+x[24])*q + x[25] #15.2 : c = (1) |O_x_c^F| = 1/2*q^18*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,15,2] = (x[23]-x[24])*q + x[25] orbit #16 : F4 dim = 48 A(O) = 1 , |A(O)_0| = 1 g_s = V[22]+V[14]+V[10]+V[2] Z_G(x)_0 = 0 # Green Polys by orbit reps #16.1 : x[25] : F4,[1] : phi[1,0] Qxi[F4,16,1] = x[25] # Green Polys by conj class in A(O) #16.1 : c = () |O_x_c^F| = q^20*(q^2-1)*(q^6-1)*(q^8-1)*(q^12-1) Qxc[F4,16,1] = x[25]