#### Green Polynomials for A7 #### W-rep key: # x[1] = [1, 1, 1, 1, 1, 1, 1, 1] , orbit = [1, 1, 1, 1, 1, 1, 1, 1] , A-rep = [] # x[2] = [2, 1, 1, 1, 1, 1, 1] , orbit = [2, 1, 1, 1, 1, 1, 1] , A-rep = [] # x[3] = [2, 2, 1, 1, 1, 1] , orbit = [2, 2, 1, 1, 1, 1] , A-rep = [] # x[4] = [2, 2, 2, 1, 1] , orbit = [2, 2, 2, 1, 1] , A-rep = [] # x[5] = [2, 2, 2, 2] , orbit = [2, 2, 2, 2] , A-rep = [] # x[6] = [3, 1, 1, 1, 1, 1] , orbit = [3, 1, 1, 1, 1, 1] , A-rep = [] # x[7] = [3, 2, 1, 1, 1] , orbit = [3, 2, 1, 1, 1] , A-rep = [] # x[8] = [3, 2, 2, 1] , orbit = [3, 2, 2, 1] , A-rep = [] # x[9] = [3, 3, 1, 1] , orbit = [3, 3, 1, 1] , A-rep = [] # x[10] = [3, 3, 2] , orbit = [3, 3, 2] , A-rep = [] # x[11] = [4, 1, 1, 1, 1] , orbit = [4, 1, 1, 1, 1] , A-rep = [] # x[12] = [4, 2, 1, 1] , orbit = [4, 2, 1, 1] , A-rep = [] # x[13] = [4, 2, 2] , orbit = [4, 2, 2] , A-rep = [] # x[14] = [4, 3, 1] , orbit = [4, 3, 1] , A-rep = [] # x[15] = [4, 4] , orbit = [4, 4] , A-rep = [] # x[16] = [5, 1, 1, 1] , orbit = [5, 1, 1, 1] , A-rep = [] # x[17] = [5, 2, 1] , orbit = [5, 2, 1] , A-rep = [] # x[18] = [5, 3] , orbit = [5, 3] , A-rep = [] # x[19] = [6, 1, 1] , orbit = [6, 1, 1] , A-rep = [] # x[20] = [6, 2] , orbit = [6, 2] , A-rep = [] # x[21] = [7, 1] , orbit = [7, 1] , A-rep = [] # x[22] = [8] , orbit = [8] , A-rep = [] ### Green Polynomials by Orbit orbit #1 : [1, 1, 1, 1, 1, 1, 1, 1] dim = 0 A(O) = 1 , |A(O)_0| = 1 g_s = 63*V[0] Z_G(x)_0 = A7 # Green Polys by orbit reps #1.1 : x[1] : [1, 1, 1, 1, 1, 1, 1, 1],[] : [8] Qxi[A7,1,1] = (x[1])*q^28 + (x[2])*q^27 + (x[2]+x[3])*q^26 + (x[2]+x[3]+x[4]+x[6])*q^25 + (x[2]+2*x[3]+x[4]+x[5]+x[6]+x[7])*q^24 + (x[2]+2*x[3]+2*x[4]+2*x[6]+2*x[7]+x[8])*q^23 + (x[2]+3*x[3]+2*x[4]+x[5]+2*x[6]+3*x[7]+2*x[8]+x[9]+x[11])*q^22 + (x[2]+2*x[3]+3*x[4]+x[5]+3*x[6]+5*x[7]+3*x[8]+x[9]+x[10]+x[11]+x[12])*q^21 + (3*x[3]+3*x[4]+2*x[5]+3*x[6]+6*x[7]+4*x[8]+3*x[9]+x[10]+2*x[11]+2*x[12]+x[13])*q^20 + (2*x[3]+4*x[4]+x[5]+3*x[6]+7*x[7]+6*x[8]+3*x[9]+2*x[10]+3*x[11]+4*x[12]+x[13]+x[14])*q^19 + (2*x[3]+3*x[4]+2*x[5]+2*x[6]+8*x[7]+7*x[8]+5*x[9]+2*x[10]+4*x[11]+5*x[12]+3*x[13]+2*x[14]+x[16])*q^18 + (x[3]+3*x[4]+x[5]+2*x[6]+8*x[7]+8*x[8]+5*x[9]+4*x[10]+4*x[11]+8*x[12]+3*x[13]+3*x[14]+x[16]+x[17])*q^17 + (x[3]+2*x[4]+2*x[5]+x[6]+7*x[7]+8*x[8]+7*x[9]+4*x[10]+5*x[11]+9*x[12]+5*x[13]+4*x[14]+x[15]+2*x[16]+2*x[17])*q^16 + (2*x[4]+x[5]+x[6]+6*x[7]+8*x[8]+6*x[9]+5*x[10]+4*x[11]+11*x[12]+5*x[13]+6*x[14]+3*x[16]+3*x[17]+x[18])*q^15 + (x[4]+x[5]+5*x[7]+7*x[8]+7*x[9]+4*x[10]+4*x[11]+10*x[12]+7*x[13]+7*x[14]+x[15]+4*x[16]+5*x[17]+x[18])*q^14 + (x[4]+3*x[7]+6*x[8]+5*x[9]+5*x[10]+3*x[11]+11*x[12]+6*x[13]+8*x[14]+x[15]+4*x[16]+6*x[17]+2*x[18]+x[19])*q^13 + (x[5]+2*x[7]+4*x[8]+5*x[9]+4*x[10]+2*x[11]+9*x[12]+7*x[13]+8*x[14]+2*x[15]+5*x[16]+7*x[17]+2*x[18]+x[19]+x[20])*q^12 + (x[7]+3*x[8]+3*x[9]+4*x[10]+x[11]+8*x[12]+5*x[13]+8*x[14]+x[15]+4*x[16]+8*x[17]+3*x[18]+2*x[19]+x[20])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+5*x[12]+5*x[13]+7*x[14]+2*x[15]+4*x[16]+8*x[17]+3*x[18]+2*x[19]+2*x[20])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+6*x[14]+x[15]+3*x[16]+7*x[17]+4*x[18]+3*x[19]+2*x[20])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+6*x[17]+3*x[18]+3*x[19]+3*x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+3*x[19]+2*x[20]+x[21])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20]+x[21])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #1.1 : c = () |O_x_c^F| = 1 Qxc[A7,1,1] = (x[1])*q^28 + (x[2])*q^27 + (x[2]+x[3])*q^26 + (x[2]+x[3]+x[4]+x[6])*q^25 + (x[2]+2*x[3]+x[4]+x[5]+x[6]+x[7])*q^24 + (x[2]+2*x[3]+2*x[4]+2*x[6]+2*x[7]+x[8])*q^23 + (x[2]+3*x[3]+2*x[4]+x[5]+2*x[6]+3*x[7]+2*x[8]+x[9]+x[11])*q^22 + (x[2]+2*x[3]+3*x[4]+x[5]+3*x[6]+5*x[7]+3*x[8]+x[9]+x[10]+x[11]+x[12])*q^21 + (3*x[3]+3*x[4]+2*x[5]+3*x[6]+6*x[7]+4*x[8]+3*x[9]+x[10]+2*x[11]+2*x[12]+x[13])*q^20 + (2*x[3]+4*x[4]+x[5]+3*x[6]+7*x[7]+6*x[8]+3*x[9]+2*x[10]+3*x[11]+4*x[12]+x[13]+x[14])*q^19 + (2*x[3]+3*x[4]+2*x[5]+2*x[6]+8*x[7]+7*x[8]+5*x[9]+2*x[10]+4*x[11]+5*x[12]+3*x[13]+2*x[14]+x[16])*q^18 + (x[3]+3*x[4]+x[5]+2*x[6]+8*x[7]+8*x[8]+5*x[9]+4*x[10]+4*x[11]+8*x[12]+3*x[13]+3*x[14]+x[16]+x[17])*q^17 + (x[3]+2*x[4]+2*x[5]+x[6]+7*x[7]+8*x[8]+7*x[9]+4*x[10]+5*x[11]+9*x[12]+5*x[13]+4*x[14]+x[15]+2*x[16]+2*x[17])*q^16 + (2*x[4]+x[5]+x[6]+6*x[7]+8*x[8]+6*x[9]+5*x[10]+4*x[11]+11*x[12]+5*x[13]+6*x[14]+3*x[16]+3*x[17]+x[18])*q^15 + (x[4]+x[5]+5*x[7]+7*x[8]+7*x[9]+4*x[10]+4*x[11]+10*x[12]+7*x[13]+7*x[14]+x[15]+4*x[16]+5*x[17]+x[18])*q^14 + (x[4]+3*x[7]+6*x[8]+5*x[9]+5*x[10]+3*x[11]+11*x[12]+6*x[13]+8*x[14]+x[15]+4*x[16]+6*x[17]+2*x[18]+x[19])*q^13 + (x[5]+2*x[7]+4*x[8]+5*x[9]+4*x[10]+2*x[11]+9*x[12]+7*x[13]+8*x[14]+2*x[15]+5*x[16]+7*x[17]+2*x[18]+x[19]+x[20])*q^12 + (x[7]+3*x[8]+3*x[9]+4*x[10]+x[11]+8*x[12]+5*x[13]+8*x[14]+x[15]+4*x[16]+8*x[17]+3*x[18]+2*x[19]+x[20])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+5*x[12]+5*x[13]+7*x[14]+2*x[15]+4*x[16]+8*x[17]+3*x[18]+2*x[19]+2*x[20])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+6*x[14]+x[15]+3*x[16]+7*x[17]+4*x[18]+3*x[19]+2*x[20])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+6*x[17]+3*x[18]+3*x[19]+3*x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+3*x[19]+2*x[20]+x[21])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20]+x[21])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #2 : [2, 1, 1, 1, 1, 1, 1] dim = 14 A(O) = 1 , |A(O)_0| = 1 g_s = 12*V[1]+V[2]+36*V[0] Z_G(x)_0 = GL6+GL1 # Green Polys by orbit reps #2.1 : x[2] : [2, 1, 1, 1, 1, 1, 1],[] : [2, 1, 1, 1, 1, 1, 1] Qxi[A7,2,1] = (x[2])*q^21 + (x[3]+x[6])*q^20 + (x[3]+x[4]+x[6]+x[7])*q^19 + (x[3]+x[4]+x[5]+x[6]+2*x[7]+x[8]+x[11])*q^18 + (x[3]+2*x[4]+x[6]+3*x[7]+2*x[8]+x[9]+x[11]+x[12])*q^17 + (x[3]+x[4]+x[5]+x[6]+4*x[7]+3*x[8]+2*x[9]+x[10]+2*x[11]+2*x[12]+x[13])*q^16 + (2*x[4]+x[5]+x[6]+4*x[7]+4*x[8]+3*x[9]+2*x[10]+2*x[11]+4*x[12]+x[13]+x[14]+x[16])*q^15 + (x[4]+x[5]+4*x[7]+5*x[8]+4*x[9]+2*x[10]+3*x[11]+5*x[12]+3*x[13]+2*x[14]+x[16]+x[17])*q^14 + (x[4]+3*x[7]+5*x[8]+4*x[9]+3*x[10]+2*x[11]+7*x[12]+3*x[13]+4*x[14]+2*x[16]+2*x[17])*q^13 + (x[5]+2*x[7]+4*x[8]+4*x[9]+3*x[10]+2*x[11]+7*x[12]+5*x[13]+5*x[14]+x[15]+3*x[16]+3*x[17]+x[18])*q^12 + (x[7]+3*x[8]+3*x[9]+4*x[10]+x[11]+7*x[12]+4*x[13]+6*x[14]+x[15]+3*x[16]+5*x[17]+x[18]+x[19])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+5*x[12]+5*x[13]+6*x[14]+x[15]+3*x[16]+6*x[17]+2*x[18]+x[19]+x[20])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+6*x[14]+x[15]+3*x[16]+6*x[17]+3*x[18]+2*x[19]+x[20])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+6*x[17]+3*x[18]+2*x[19]+2*x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+3*x[19]+2*x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20]+x[21])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #2.1 : c = () |O_x_c^F| = (q^6+q^5+q^4+q^3+q^2+q+1)*(q^8-1) Qxc[A7,2,1] = (x[2])*q^21 + (x[3]+x[6])*q^20 + (x[3]+x[4]+x[6]+x[7])*q^19 + (x[3]+x[4]+x[5]+x[6]+2*x[7]+x[8]+x[11])*q^18 + (x[3]+2*x[4]+x[6]+3*x[7]+2*x[8]+x[9]+x[11]+x[12])*q^17 + (x[3]+x[4]+x[5]+x[6]+4*x[7]+3*x[8]+2*x[9]+x[10]+2*x[11]+2*x[12]+x[13])*q^16 + (2*x[4]+x[5]+x[6]+4*x[7]+4*x[8]+3*x[9]+2*x[10]+2*x[11]+4*x[12]+x[13]+x[14]+x[16])*q^15 + (x[4]+x[5]+4*x[7]+5*x[8]+4*x[9]+2*x[10]+3*x[11]+5*x[12]+3*x[13]+2*x[14]+x[16]+x[17])*q^14 + (x[4]+3*x[7]+5*x[8]+4*x[9]+3*x[10]+2*x[11]+7*x[12]+3*x[13]+4*x[14]+2*x[16]+2*x[17])*q^13 + (x[5]+2*x[7]+4*x[8]+4*x[9]+3*x[10]+2*x[11]+7*x[12]+5*x[13]+5*x[14]+x[15]+3*x[16]+3*x[17]+x[18])*q^12 + (x[7]+3*x[8]+3*x[9]+4*x[10]+x[11]+7*x[12]+4*x[13]+6*x[14]+x[15]+3*x[16]+5*x[17]+x[18]+x[19])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+5*x[12]+5*x[13]+6*x[14]+x[15]+3*x[16]+6*x[17]+2*x[18]+x[19]+x[20])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+6*x[14]+x[15]+3*x[16]+6*x[17]+3*x[18]+2*x[19]+x[20])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+6*x[17]+3*x[18]+2*x[19]+2*x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+3*x[19]+2*x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20]+x[21])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #3 : [2, 2, 1, 1, 1, 1] dim = 24 A(O) = 1 , |A(O)_0| = 1 g_s = 4*V[2]+16*V[1]+19*V[0] Z_G(x)_0 = GL4+GL2 # Green Polys by orbit reps #3.1 : x[3] : [2, 2, 1, 1, 1, 1],[] : [2, 2, 1, 1, 1, 1] Qxi[A7,3,1] = (x[3])*q^16 + (x[4]+x[6]+x[7])*q^15 + (x[4]+x[5]+2*x[7]+x[8]+x[9]+x[11])*q^14 + (x[4]+2*x[7]+3*x[8]+x[9]+x[10]+x[11]+2*x[12])*q^13 + (x[5]+2*x[7]+3*x[8]+3*x[9]+x[10]+x[11]+3*x[12]+2*x[13]+x[14]+x[16])*q^12 + (x[7]+3*x[8]+2*x[9]+3*x[10]+x[11]+5*x[12]+2*x[13]+3*x[14]+x[16]+x[17])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+4*x[12]+4*x[13]+4*x[14]+x[15]+2*x[16]+3*x[17])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+5*x[14]+2*x[16]+4*x[17]+2*x[18]+x[19])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+5*x[17]+2*x[18]+x[19]+x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+2*x[19]+x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #3.1 : c = () |O_x_c^F| = q*(q^2+q+1)*(q^2-q+1)*(q^4+q^3+q^2+q+1)*(q^7-1)*(q^8-1) Qxc[A7,3,1] = (x[3])*q^16 + (x[4]+x[6]+x[7])*q^15 + (x[4]+x[5]+2*x[7]+x[8]+x[9]+x[11])*q^14 + (x[4]+2*x[7]+3*x[8]+x[9]+x[10]+x[11]+2*x[12])*q^13 + (x[5]+2*x[7]+3*x[8]+3*x[9]+x[10]+x[11]+3*x[12]+2*x[13]+x[14]+x[16])*q^12 + (x[7]+3*x[8]+2*x[9]+3*x[10]+x[11]+5*x[12]+2*x[13]+3*x[14]+x[16]+x[17])*q^11 + (2*x[8]+3*x[9]+2*x[10]+x[11]+4*x[12]+4*x[13]+4*x[14]+x[15]+2*x[16]+3*x[17])*q^10 + (x[8]+x[9]+2*x[10]+4*x[12]+3*x[13]+5*x[14]+2*x[16]+4*x[17]+2*x[18]+x[19])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+4*x[14]+2*x[15]+2*x[16]+5*x[17]+2*x[18]+x[19]+x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+5*x[17]+3*x[18]+2*x[19]+x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+3*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #4 : [2, 2, 2, 1, 1] dim = 30 A(O) = 1 , |A(O)_0| = 1 g_s = 9*V[2]+12*V[1]+12*V[0] Z_G(x)_0 = GL3+GL2 # Green Polys by orbit reps #4.1 : x[4] : [2, 2, 2, 1, 1],[] : [2, 2, 2, 1, 1] Qxi[A7,4,1] = (x[4])*q^13 + (x[5]+x[7]+x[8])*q^12 + (x[7]+2*x[8]+x[9]+x[10]+x[12])*q^11 + (2*x[8]+2*x[9]+x[10]+x[11]+2*x[12]+2*x[13]+x[14])*q^10 + (x[8]+x[9]+2*x[10]+3*x[12]+2*x[13]+3*x[14]+x[16]+x[17])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+3*x[14]+x[15]+x[16]+3*x[17]+x[18])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+4*x[17]+2*x[18]+x[19])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+x[19]+2*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #4.1 : c = () |O_x_c^F| = q^3*(q^4+q^3+q^2+q+1)*(q^2+1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,4,1] = (x[4])*q^13 + (x[5]+x[7]+x[8])*q^12 + (x[7]+2*x[8]+x[9]+x[10]+x[12])*q^11 + (2*x[8]+2*x[9]+x[10]+x[11]+2*x[12]+2*x[13]+x[14])*q^10 + (x[8]+x[9]+2*x[10]+3*x[12]+2*x[13]+3*x[14]+x[16]+x[17])*q^9 + (x[9]+x[10]+2*x[12]+3*x[13]+3*x[14]+x[15]+x[16]+3*x[17]+x[18])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+4*x[17]+2*x[18]+x[19])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+x[19]+2*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #5 : [2, 2, 2, 2] dim = 32 A(O) = 1 , |A(O)_0| = 1 g_s = 16*V[2]+15*V[0] Z_G(x)_0 = GL4 # Green Polys by orbit reps #5.1 : x[5] : [2, 2, 2, 2],[] : [2, 2, 2, 2] Qxi[A7,5,1] = (x[5])*q^12 + (x[8])*q^11 + (x[8]+x[9]+x[13])*q^10 + (x[8]+x[10]+x[12]+x[13]+x[14])*q^9 + (x[9]+x[10]+x[12]+2*x[13]+x[14]+x[15]+x[17])*q^8 + (x[10]+x[12]+x[13]+2*x[14]+2*x[17]+x[18])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+2*x[17]+x[18]+x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #5.1 : c = () |O_x_c^F| = q^6*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,5,1] = (x[5])*q^12 + (x[8])*q^11 + (x[8]+x[9]+x[13])*q^10 + (x[8]+x[10]+x[12]+x[13]+x[14])*q^9 + (x[9]+x[10]+x[12]+2*x[13]+x[14]+x[15]+x[17])*q^8 + (x[10]+x[12]+x[13]+2*x[14]+2*x[17]+x[18])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+2*x[17]+x[18]+x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #6 : [3, 1, 1, 1, 1, 1] dim = 26 A(O) = 1 , |A(O)_0| = 1 g_s = V[4]+11*V[2]+25*V[0] Z_G(x)_0 = GL5+GL1 # Green Polys by orbit reps #6.1 : x[6] : [3, 1, 1, 1, 1, 1],[] : [3, 1, 1, 1, 1, 1] Qxi[A7,6,1] = (x[6])*q^15 + (x[7]+x[11])*q^14 + (x[7]+x[8]+x[11]+x[12])*q^13 + (x[7]+x[8]+x[9]+x[11]+2*x[12]+x[13]+x[16])*q^12 + (x[7]+x[8]+x[9]+x[10]+x[11]+3*x[12]+x[13]+x[14]+x[16]+x[17])*q^11 + (x[8]+2*x[9]+x[10]+x[11]+3*x[12]+2*x[13]+2*x[14]+2*x[16]+2*x[17])*q^10 + (x[8]+x[9]+x[10]+3*x[12]+2*x[13]+3*x[14]+2*x[16]+3*x[17]+x[18]+x[19])*q^9 + (x[9]+x[10]+2*x[12]+2*x[13]+3*x[14]+x[15]+2*x[16]+4*x[17]+x[18]+x[19]+x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+4*x[17]+2*x[18]+2*x[19]+x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+2*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #6.1 : c = () |O_x_c^F| = q^6*(q^2+q+1)*(q^3+1)*(q^7-1)*(q^8-1) Qxc[A7,6,1] = (x[6])*q^15 + (x[7]+x[11])*q^14 + (x[7]+x[8]+x[11]+x[12])*q^13 + (x[7]+x[8]+x[9]+x[11]+2*x[12]+x[13]+x[16])*q^12 + (x[7]+x[8]+x[9]+x[10]+x[11]+3*x[12]+x[13]+x[14]+x[16]+x[17])*q^11 + (x[8]+2*x[9]+x[10]+x[11]+3*x[12]+2*x[13]+2*x[14]+2*x[16]+2*x[17])*q^10 + (x[8]+x[9]+x[10]+3*x[12]+2*x[13]+3*x[14]+2*x[16]+3*x[17]+x[18]+x[19])*q^9 + (x[9]+x[10]+2*x[12]+2*x[13]+3*x[14]+x[15]+2*x[16]+4*x[17]+x[18]+x[19]+x[20])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+4*x[17]+2*x[18]+2*x[19]+x[20])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+2*x[19]+2*x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20]+x[21])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #7 : [3, 2, 1, 1, 1] dim = 34 A(O) = 1 , |A(O)_0| = 1 g_s = V[4]+2*V[3]+8*V[2]+8*V[1]+10*V[0] Z_G(x)_0 = GL3+2*GL1 # Green Polys by orbit reps #7.1 : x[7] : [3, 2, 1, 1, 1],[] : [3, 2, 1, 1, 1] Qxi[A7,7,1] = (x[7])*q^11 + (x[8]+x[9]+x[11]+x[12])*q^10 + (x[8]+x[9]+x[10]+2*x[12]+x[13]+x[14]+x[16])*q^9 + (x[9]+x[10]+2*x[12]+2*x[13]+2*x[14]+x[16]+2*x[17])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+3*x[17]+x[18]+x[19])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+x[19]+x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #7.1 : c = () |O_x_c^F| = q^6*(q^4+q^3+q^2+q+1)*(q+1)*(q^2+1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,7,1] = (x[7])*q^11 + (x[8]+x[9]+x[11]+x[12])*q^10 + (x[8]+x[9]+x[10]+2*x[12]+x[13]+x[14]+x[16])*q^9 + (x[9]+x[10]+2*x[12]+2*x[13]+2*x[14]+x[16]+2*x[17])*q^8 + (x[10]+x[12]+x[13]+3*x[14]+x[15]+x[16]+3*x[17]+x[18]+x[19])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+3*x[17]+2*x[18]+x[19]+x[20])*q^6 + (x[14]+2*x[17]+2*x[18]+2*x[19]+2*x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #8 : [3, 2, 2, 1] dim = 38 A(O) = 1 , |A(O)_0| = 1 g_s = V[4]+4*V[3]+7*V[2]+8*V[1]+5*V[0] Z_G(x)_0 = GL2+2*GL1 # Green Polys by orbit reps #8.1 : x[8] : [3, 2, 2, 1],[] : [3, 2, 2, 1] Qxi[A7,8,1] = (x[8])*q^9 + (x[9]+x[10]+x[12]+x[13])*q^8 + (x[10]+x[12]+x[13]+2*x[14]+x[17])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+2*x[17]+x[18])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #8.1 : c = () |O_x_c^F| = q^7*(q^2+q+1)*(q+1)*(q^2+1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,8,1] = (x[8])*q^9 + (x[9]+x[10]+x[12]+x[13])*q^8 + (x[10]+x[12]+x[13]+2*x[14]+x[17])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+2*x[17]+x[18])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #9 : [3, 3, 1, 1] dim = 40 A(O) = 1 , |A(O)_0| = 1 g_s = 4*V[4]+12*V[2]+7*V[0] Z_G(x)_0 = 2*GL2 # Green Polys by orbit reps #9.1 : x[9] : [3, 3, 1, 1],[] : [3, 3, 1, 1] Qxi[A7,9,1] = (x[9])*q^8 + (x[10]+x[12]+x[14])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+x[17])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #9.1 : c = () |O_x_c^F| = q^10*(q^2+q+1)*(q^2+1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,9,1] = (x[9])*q^8 + (x[10]+x[12]+x[14])*q^7 + (x[13]+2*x[14]+x[15]+x[16]+x[17])*q^6 + (x[14]+2*x[17]+2*x[18]+x[19])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #10 : [3, 3, 2] dim = 42 A(O) = 1 , |A(O)_0| = 1 g_s = 4*V[4]+4*V[3]+5*V[2]+4*V[1]+4*V[0] Z_G(x)_0 = GL2+GL1 # Green Polys by orbit reps #10.1 : x[10] : [3, 3, 2],[] : [3, 3, 2] Qxi[A7,10,1] = (x[10])*q^7 + (x[13]+x[14])*q^6 + (x[14]+x[17]+x[18])*q^5 + (x[15]+x[17]+x[18]+x[20])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #10.1 : c = () |O_x_c^F| = q^10*(q^2+q+1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,10,1] = (x[10])*q^7 + (x[13]+x[14])*q^6 + (x[14]+x[17]+x[18])*q^5 + (x[15]+x[17]+x[18]+x[20])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #11 : [4, 1, 1, 1, 1] dim = 36 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+V[4]+8*V[3]+V[2]+16*V[0] Z_G(x)_0 = GL4+GL1 # Green Polys by orbit reps #11.1 : x[11] : [4, 1, 1, 1, 1],[] : [4, 1, 1, 1, 1] Qxi[A7,11,1] = (x[11])*q^10 + (x[12]+x[16])*q^9 + (x[12]+x[13]+x[16]+x[17])*q^8 + (x[12]+x[14]+x[16]+2*x[17]+x[19])*q^7 + (x[13]+x[14]+x[16]+2*x[17]+x[18]+x[19]+x[20])*q^6 + (x[14]+2*x[17]+x[18]+2*x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #11.1 : c = () |O_x_c^F| = q^11*(q^4+q^3+q^2+q+1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,11,1] = (x[11])*q^10 + (x[12]+x[16])*q^9 + (x[12]+x[13]+x[16]+x[17])*q^8 + (x[12]+x[14]+x[16]+2*x[17]+x[19])*q^7 + (x[13]+x[14]+x[16]+2*x[17]+x[18]+x[19]+x[20])*q^6 + (x[14]+2*x[17]+x[18]+2*x[19]+x[20])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20]+x[21])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #12 : [4, 2, 1, 1] dim = 42 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+3*V[4]+4*V[3]+4*V[2]+4*V[1]+5*V[0] Z_G(x)_0 = GL2+2*GL1 # Green Polys by orbit reps #12.1 : x[12] : [4, 2, 1, 1],[] : [4, 2, 1, 1] Qxi[A7,12,1] = (x[12])*q^7 + (x[13]+x[14]+x[16]+x[17])*q^6 + (x[14]+2*x[17]+x[18]+x[19])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #12.1 : c = () |O_x_c^F| = q^11*(q^2+q+1)*(q+1)*(q^2+1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,12,1] = (x[12])*q^7 + (x[13]+x[14]+x[16]+x[17])*q^6 + (x[14]+2*x[17]+x[18]+x[19])*q^5 + (x[15]+x[17]+x[18]+x[19]+2*x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #13 : [4, 2, 2] dim = 44 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+5*V[4]+9*V[2]+4*V[0] Z_G(x)_0 = GL2+GL1 # Green Polys by orbit reps #13.1 : x[13] : [4, 2, 2],[] : [4, 2, 2] Qxi[A7,13,1] = (x[13])*q^6 + (x[14]+x[17])*q^5 + (x[15]+x[17]+x[18]+x[20])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #13.1 : c = () |O_x_c^F| = q^12*(q^2+q+1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,13,1] = (x[13])*q^6 + (x[14]+x[17])*q^5 + (x[15]+x[17]+x[18]+x[20])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #14 : [4, 3, 1] dim = 46 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+2*V[5]+2*V[4]+4*V[3]+4*V[2]+2*V[1]+2*V[0] Z_G(x)_0 = 3*GL1 # Green Polys by orbit reps #14.1 : x[14] : [4, 3, 1],[] : [4, 3, 1] Qxi[A7,14,1] = (x[14])*q^5 + (x[15]+x[17]+x[18])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #14.1 : c = () |O_x_c^F| = q^13*(q^2+q+1)*(q+1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,14,1] = (x[14])*q^5 + (x[15]+x[17]+x[18])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #15 : [4, 4] dim = 48 A(O) = 1 , |A(O)_0| = 1 g_s = 4*V[6]+4*V[4]+4*V[2]+3*V[0] Z_G(x)_0 = GL2 # Green Polys by orbit reps #15.1 : x[15] : [4, 4],[] : [4, 4] Qxi[A7,15,1] = (x[15])*q^4 + (x[18])*q^3 + (x[20])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #15.1 : c = () |O_x_c^F| = q^15*(q^3-1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,15,1] = (x[15])*q^4 + (x[18])*q^3 + (x[20])*q^2 + (x[21])*q + x[22] orbit #16 : [5, 1, 1, 1] dim = 44 A(O) = 1 , |A(O)_0| = 1 g_s = V[8]+V[6]+7*V[4]+V[2]+9*V[0] Z_G(x)_0 = GL3+GL1 # Green Polys by orbit reps #16.1 : x[16] : [5, 1, 1, 1],[] : [5, 1, 1, 1] Qxi[A7,16,1] = (x[16])*q^6 + (x[17]+x[19])*q^5 + (x[17]+x[19]+x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #16.1 : c = () |O_x_c^F| = q^15*(q+1)*(q^2+1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,16,1] = (x[16])*q^6 + (x[17]+x[19])*q^5 + (x[17]+x[19]+x[20])*q^4 + (x[18]+x[19]+x[20]+x[21])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #17 : [5, 2, 1] dim = 48 A(O) = 1 , |A(O)_0| = 1 g_s = V[8]+V[6]+2*V[5]+3*V[4]+2*V[3]+2*V[2]+2*V[1]+2*V[0] Z_G(x)_0 = 3*GL1 # Green Polys by orbit reps #17.1 : x[17] : [5, 2, 1],[] : [5, 2, 1] Qxi[A7,17,1] = (x[17])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #17.1 : c = () |O_x_c^F| = q^15*(q^2+q+1)*(q+1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,17,1] = (x[17])*q^4 + (x[18]+x[19]+x[20])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #18 : [5, 3] dim = 50 A(O) = 1 , |A(O)_0| = 1 g_s = V[8]+3*V[6]+4*V[4]+4*V[2]+V[0] Z_G(x)_0 = 2*GL1 # Green Polys by orbit reps #18.1 : x[18] : [5, 3],[] : [5, 3] Qxi[A7,18,1] = (x[18])*q^3 + (x[20])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #18.1 : c = () |O_x_c^F| = q^16*(q+1)*(q^3-1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,18,1] = (x[18])*q^3 + (x[20])*q^2 + (x[21])*q + x[22] orbit #19 : [6, 1, 1] dim = 50 A(O) = 1 , |A(O)_0| = 1 g_s = V[10]+V[8]+V[6]+4*V[5]+V[4]+V[2]+4*V[0] Z_G(x)_0 = GL2+GL1 # Green Polys by orbit reps #19.1 : x[19] : [6, 1, 1],[] : [6, 1, 1] Qxi[A7,19,1] = (x[19])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #19.1 : c = () |O_x_c^F| = q^18*(q^2+q+1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,19,1] = (x[19])*q^3 + (x[20]+x[21])*q^2 + (x[21])*q + x[22] orbit #20 : [6, 2] dim = 52 A(O) = 1 , |A(O)_0| = 1 g_s = V[10]+V[8]+3*V[6]+3*V[4]+2*V[2]+V[0] Z_G(x)_0 = 2*GL1 # Green Polys by orbit reps #20.1 : x[20] : [6, 2],[] : [6, 2] Qxi[A7,20,1] = (x[20])*q^2 + (x[21])*q + x[22] # Green Polys by conj class in A(O) #20.1 : c = () |O_x_c^F| = q^18*(q+1)*(q^3-1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,20,1] = (x[20])*q^2 + (x[21])*q + x[22] orbit #21 : [7, 1] dim = 54 A(O) = 1 , |A(O)_0| = 1 g_s = V[12]+V[10]+V[8]+3*V[6]+V[4]+V[2]+V[0] Z_G(x)_0 = 2*GL1 # Green Polys by orbit reps #21.1 : x[21] : [7, 1],[] : [7, 1] Qxi[A7,21,1] = (x[21])*q + x[22] # Green Polys by conj class in A(O) #21.1 : c = () |O_x_c^F| = q^20*(q+1)*(q^3-1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,21,1] = (x[21])*q + x[22] orbit #22 : [8] dim = 56 A(O) = 1 , |A(O)_0| = 1 g_s = V[14]+V[12]+V[10]+V[8]+V[6]+V[4]+V[2] Z_G(x)_0 = GL1 # Green Polys by orbit reps #22.1 : x[22] : [8],[] : [8] Qxi[A7,22,1] = x[22] # Green Polys by conj class in A(O) #22.1 : c = () |O_x_c^F| = q^21*(q^2-1)*(q^3-1)*(q^4-1)*(q^5-1)*(q^6-1)*(q^7-1)*(q^8-1) Qxc[A7,22,1] = x[22]