# Character: X6 # Comment: rho-split Young rep # Ind: 0 # Ring: C # Sparsity: 3% # Checker result: pass # Conjugacy class representative result: pass local b, B, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** i := E(4); result.comment := "A8 as 21 x 21 matrices\n"; result.generators := [ [[3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+2/5*E(15)^7+3/5*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+1/3*E(15)^8,-E(15)-E(15)^2-E(15)^4-2/3*E(15)^7-E(15)^8-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+17/30*E(15)^7+3/5*E(15)^8+17/30*E(15)^11+17/30*E(15)^13+17/30*E(15)^14, 17/30*E(15)+17/30*E(15)^2+17/30*E(15)^4+3/5*E(15)^7+17/30*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, -7/5*E(15)-7/5*E(15)^2-7/5*E(15)^4-8/5*E(15)^7-7/5*E(15)^8-8/5*E(15)^11-8/5*E(15)^13-8/5*E(15)^14, 4/3*E(15)+4/3*E(15)^2+4/3*E(15)^4+E(15)^7+4/3*E(15)^8+E(15)^11+E(15)^13+E(15)^14, 1/3*E(15)^7+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14,-1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4-2/15*E(15)^7-1/5*E(15)^8-2/15*E(15)^11-2/15*E(15)^13-2/15*E(15)^14, -41/15*E(15)-41/15*E(15)^2-41/15*E(15)^4-18/5*E(15)^7-41/15*E(15)^8-18/5*E(15)^11-18/5*E(15)^13-18/5*E(15)^14, 17/30*E(15)+17/30*E(15)^2+17/30*E(15)^4+43/30*E(15)^7+17/30*E(15)^8+43/30*E(15)^11+43/30*E(15)^13+43/30*E(15)^14, 23/30*E(15)+23/30*E(15)^2+23/30*E(15)^4+11/15*E(15)^7+23/30*E(15)^8+11/15*E(15)^11+11/15*E(15)^13+11/15*E(15)^14, -34/15*E(15)-34/15*E(15)^2-34/15*E(15)^4-97/30*E(15)^7-34/15*E(15)^8-97/30*E(15)^11-97/30*E(15)^13-97/30*E(15)^14, -8/15*E(15)-8/15*E(15)^2-8/15*E(15)^4-7/15*E(15)^7-8/15*E(15)^8-7/15*E(15)^11-7/15*E(15)^13-7/15*E(15)^14, 44/15*E(15)+44/15*E(15)^2+44/15*E(15)^4+61/15*E(15)^7+44/15*E(15)^8+61/15*E(15)^11+61/15*E(15)^13+61/15*E(15)^14, -73/30*E(15)-73/30*E(15)^2-73/30*E(15)^4-107/30*E(15)^7-73/30*E(15)^8-107/30*E(15)^11-107/30*E(15)^13-107/30*E(15)^14, -2,8/3*E(15)+8/3*E(15)^2+8/3*E(15)^4+10/3*E(15)^7+8/3*E(15)^8+10/3*E(15)^11+10/3*E(15)^13+10/3*E(15)^14, 3/2,-23/6*E(15)-23/6*E(15)^2-23/6*E(15)^4-31/6*E(15)^7-23/6*E(15)^8-31/6*E(15)^11-31/6*E(15)^13-31/6*E(15)^14, 11/3*E(15)+11/3*E(15)^2+11/3*E(15)^4+13/3*E(15)^7+11/3*E(15)^8+13/3*E(15)^11+13/3*E(15)^13+13/3*E(15)^14 ], [-3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-2/5*E(15)^7-3/5*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, 1/15*E(15)+1/15*E(15)^2+1/15*E(15)^4+4/15*E(15)^7+1/15*E(15)^8+4/15*E(15)^11+4/15*E(15)^13+4/15*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+1/3*E(15)^8,-8/15*E(15)-8/15*E(15)^2-8/15*E(15)^4-3/10*E(15)^7-8/15*E(15)^8-3/10*E(15)^11-3/10*E(15)^13-3/10*E(15)^14, -17/30*E(15)-17/30*E(15)^2-17/30*E(15)^4-4/15*E(15)^7-17/30*E(15)^8-4/15*E(15)^11-4/15*E(15)^13-4/15*E(15)^14, 7/5*E(15)+7/5*E(15)^2+7/5*E(15)^4+8/5*E(15)^7+7/5*E(15)^8+8/5*E(15)^11+8/5*E(15)^13+8/5*E(15)^14, -14/15*E(15)-14/15*E(15)^2-14/15*E(15)^4-11/15*E(15)^7-14/15*E(15)^8-11/15*E(15)^11-11/15*E(15)^13-11/15*E(15)^14, -2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-E(15)^7-2/3*E(15)^8-E(15)^11-E(15)^13-E(15)^14, 4/15*E(15)+4/15*E(15)^2+4/15*E(15)^4+2/5*E(15)^7+4/15*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, 41/15*E(15)+41/15*E(15)^2+41/15*E(15)^4+29/15*E(15)^7+41/15*E(15)^8+29/15*E(15)^11+29/15*E(15)^13+29/15*E(15)^14, -37/30*E(15)-37/30*E(15)^2-37/30*E(15)^4-23/30*E(15)^7-37/30*E(15)^8-23/30*E(15)^11-23/30*E(15)^13-23/30*E(15)^14, 3/10*E(15)+3/10*E(15)^2+3/10*E(15)^4+1/5*E(15)^7+3/10*E(15)^8+1/5*E(15)^11+1/5*E(15)^13+1/5*E(15)^14, 34/15*E(15)+34/15*E(15)^2+34/15*E(15)^4+67/30*E(15)^7+34/15*E(15)^8+67/30*E(15)^11+67/30*E(15)^13+67/30*E(15)^14, -2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-3/5*E(15)^7-2/5*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, -44/15*E(15)-44/15*E(15)^2-44/15*E(15)^4-31/15*E(15)^7-44/15*E(15)^8-31/15*E(15)^11-31/15*E(15)^13-31/15*E(15)^14, 53/30*E(15)+53/30*E(15)^2+53/30*E(15)^4+37/30*E(15)^7+53/30*E(15)^8+37/30*E(15)^11+37/30*E(15)^13+37/30*E(15)^14, -1,-4/3*E(15)-4/3*E(15)^2-4/3*E(15)^4-5/3*E(15)^7-4/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, 1/2,19/6*E(15)+19/6*E(15)^2+19/6*E(15)^4+17/6*E(15)^7+19/6*E(15)^8+17/6*E(15)^11+17/6*E(15)^13+17/6*E(15)^14, -4/3*E(15)-4/3*E(15)^2-4/3*E(15)^4-2/3*E(15)^7-4/3*E(15)^8-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14 ], [-16/15*E(15)-16/15*E(15)^2-16/15*E(15)^4-14/15*E(15)^7-16/15*E(15)^8-14/15*E(15)^11-14/15*E(15)^13-14/15*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+2/3*E(15)^7+1/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+2/5*E(15)^7+3/5*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, -2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-1/10*E(15)^7-2/5*E(15)^8-1/10*E(15)^11-1/10*E(15)^13-1/10*E(15)^14, -1,29/15*E(15)+29/15*E(15)^2+29/15*E(15)^4+31/15*E(15)^7+29/15*E(15)^8+31/15*E(15)^11+31/15*E(15)^13+31/15*E(15)^14, -5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-4/3*E(15)^7-5/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14, -7/5*E(15)-7/5*E(15)^2-7/5*E(15)^4-8/5*E(15)^7-7/5*E(15)^8-8/5*E(15)^11-8/5*E(15)^13-8/5*E(15)^14, -1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4+1/5*E(15)^7-1/5*E(15)^8+1/5*E(15)^11+1/5*E(15)^13+1/5*E(15)^14, 53/15*E(15)+53/15*E(15)^2+53/15*E(15)^4+52/15*E(15)^7+53/15*E(15)^8+52/15*E(15)^11+52/15*E(15)^13+52/15*E(15)^14, -19/15*E(15)-19/15*E(15)^2-19/15*E(15)^4-37/30*E(15)^7-19/15*E(15)^8-37/30*E(15)^11-37/30*E(15)^13-37/30*E(15)^14, -2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-3/5*E(15)^7-2/5*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, 4*E(15)+4*E(15)^2+4*E(15)^4+9/2*E(15)^7+4*E(15)^8+9/2*E(15)^11+9/2*E(15)^13+9/2*E(15)^14, 4/5*E(15)+4/5*E(15)^2+4/5*E(15)^4+1/5*E(15)^7+4/5*E(15)^8+1/5*E(15)^11+1/5*E(15)^13+1/5*E(15)^14, -67/15*E(15)-67/15*E(15)^2-67/15*E(15)^4-68/15*E(15)^7-67/15*E(15)^8-68/15*E(15)^11-68/15*E(15)^13-68/15*E(15)^14, 56/15*E(15)+56/15*E(15)^2+56/15*E(15)^4+113/30*E(15)^7+56/15*E(15)^8+113/30*E(15)^11+113/30*E(15)^13+113/30*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+2/3*E(15)^7+1/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, -11/3*E(15)-11/3*E(15)^2-11/3*E(15)^4-13/3*E(15)^7-11/3*E(15)^8-13/3*E(15)^11-13/3*E(15)^13-13/3*E(15)^14, -5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-11/6*E(15)^7-5/3*E(15)^8-11/6*E(15)^11-11/6*E(15)^13-11/6*E(15)^14, 16/3*E(15)+16/3*E(15)^2+16/3*E(15)^4+37/6*E(15)^7+16/3*E(15)^8+37/6*E(15)^11+37/6*E(15)^13+37/6*E(15)^14, -4], [-3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-2/5*E(15)^7-3/5*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, -1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4-2/15*E(15)^7-1/5*E(15)^8-2/15*E(15)^11-2/15*E(15)^13-2/15*E(15)^14, 8/15*E(15)+8/15*E(15)^2+8/15*E(15)^4+2/15*E(15)^7+8/15*E(15)^8+2/15*E(15)^11+2/15*E(15)^13+2/15*E(15)^14, -2/15*E(15)-2/15*E(15)^2-2/15*E(15)^4-1/30*E(15)^7-2/15*E(15)^8-1/30*E(15)^11-1/30*E(15)^13-1/30*E(15)^14, -7/10*E(15)-7/10*E(15)^2-7/10*E(15)^4-7/15*E(15)^7-7/10*E(15)^8-7/15*E(15)^11-7/15*E(15)^13-7/15*E(15)^14, 2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+3/5*E(15)^7+2/5*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, -1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4-2/15*E(15)^7-1/5*E(15)^8-2/15*E(15)^11-2/15*E(15)^13-2/15*E(15)^14, -7/15*E(15)-7/15*E(15)^2-7/15*E(15)^4+2/15*E(15)^7-7/15*E(15)^8+2/15*E(15)^11+2/15*E(15)^13+2/15*E(15)^14, -1/3,8/5*E(15)+8/5*E(15)^2+8/5*E(15)^4+26/15*E(15)^7+8/5*E(15)^8+26/15*E(15)^11+26/15*E(15)^13+26/15*E(15)^14, -17/30*E(15)-17/30*E(15)^2-17/30*E(15)^4-43/30*E(15)^7-17/30*E(15)^8-43/30*E(15)^11-43/30*E(15)^13-43/30*E(15)^14, -13/10*E(15)-13/10*E(15)^2-13/10*E(15)^4-6/5*E(15)^7-13/10*E(15)^8-6/5*E(15)^11-6/5*E(15)^13-6/5*E(15)^14, 32/15*E(15)+32/15*E(15)^2+32/15*E(15)^4+41/30*E(15)^7+32/15*E(15)^8+41/30*E(15)^11+41/30*E(15)^13+41/30*E(15)^14, 1,-31/15*E(15)-31/15*E(15)^2-31/15*E(15)^4-29/15*E(15)^7-31/15*E(15)^8-29/15*E(15)^11-29/15*E(15)^13-29/15*E(15)^14, 73/30*E(15)+73/30*E(15)^2+73/30*E(15)^4+77/30*E(15)^7+73/30*E(15)^8+77/30*E(15)^11+77/30*E(15)^13+77/30*E(15)^14, 2,-5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-4/3*E(15)^7-5/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14, -5/2,17/6*E(15)+17/6*E(15)^2+17/6*E(15)^4+19/6*E(15)^7+17/6*E(15)^8+19/6*E(15)^11+19/6*E(15)^13+19/6*E(15)^14, -8/3*E(15)-8/3*E(15)^2-8/3*E(15)^4-10/3*E(15)^7-8/3*E(15)^8-10/3*E(15)^11-10/3*E(15)^13-10/3*E(15)^14 ], [-11/15*E(15)-11/15*E(15)^2-11/15*E(15)^4-4/15*E(15)^7-11/15*E(15)^8-4/15*E(15)^11-4/15*E(15)^13-4/15*E(15)^14, 7/15*E(15)+7/15*E(15)^2+7/15*E(15)^4+8/15*E(15)^7+7/15*E(15)^8+8/15*E(15)^11+8/15*E(15)^13+8/15*E(15)^14, 1/5*E(15)+1/5*E(15)^2+1/5*E(15)^4-1/5*E(15)^7+1/5*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, 2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+3/5*E(15)^7+2/5*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, -9/10*E(15)-9/10*E(15)^2-9/10*E(15)^4-3/5*E(15)^7-9/10*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, 19/15*E(15)+19/15*E(15)^2+19/15*E(15)^4+11/15*E(15)^7+19/15*E(15)^8+11/15*E(15)^11+11/15*E(15)^13+11/15*E(15)^14, -8/15*E(15)-8/15*E(15)^2-8/15*E(15)^4-7/15*E(15)^7-8/15*E(15)^8-7/15*E(15)^11-7/15*E(15)^13-7/15*E(15)^14, -4/5*E(15)-4/5*E(15)^2-4/5*E(15)^4-1/5*E(15)^7-4/5*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, -2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-3/5*E(15)^7-2/5*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, 37/15*E(15)+37/15*E(15)^2+37/15*E(15)^4+23/15*E(15)^7+37/15*E(15)^8+23/15*E(15)^11+23/15*E(15)^13+23/15*E(15)^14, -43/30*E(15)-43/30*E(15)^2-43/30*E(15)^4-31/15*E(15)^7-43/30*E(15)^8-31/15*E(15)^11-31/15*E(15)^13-31/15*E(15)^14, -11/10*E(15)-11/10*E(15)^2-11/10*E(15)^4-2/5*E(15)^7-11/10*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, 13/5*E(15)+13/5*E(15)^2+13/5*E(15)^4+7/5*E(15)^7+13/5*E(15)^8+7/5*E(15)^11+7/5*E(15)^13+7/5*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+2/5*E(15)^7+3/5*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, 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-1/6*E(15)-1/6*E(15)^2-1/6*E(15)^4-1/3*E(15)^7-1/6*E(15)^8-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14, 0,-2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4+1/6*E(15)^7-2/3*E(15)^8+1/6*E(15)^11+1/6*E(15)^13+1/6*E(15)^14, -1/6*E(15)-1/6*E(15)^2-1/6*E(15)^4-5/6*E(15)^7-1/6*E(15)^8-5/6*E(15)^11-5/6*E(15)^13-5/6*E(15)^14, -1/3*E(15)-1/3*E(15)^2-1/3*E(15)^4-2/3*E(15)^7-1/3*E(15)^8-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14, -1/6*E(15)-1/6*E(15)^2-1/6*E(15)^4+2/3*E(15)^7-1/6*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 2/3,1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4-1/2*E(15)^7+1/3*E(15)^8-1/2*E(15)^11-1/2*E(15)^13-1/2*E(15)^14, 1/6*E(15)+1/6*E(15)^2+1/6*E(15)^4+E(15)^7+1/6*E(15)^8+E(15)^11+E(15)^13+E(15)^14, -1/2,1/6*E(15)+1/6*E(15)^2+1/6*E(15)^4+1/6*E(15)^8,1/2*E(15)+1/2*E(15)^2+1/2*E(15)^4+1/6*E(15)^7+1/2*E(15)^8+1/6*E(15)^11+1/6*E(15)^13+1/6*E(15)^14, -E(15)-E(15)^2-E(15)^4-1/6*E(15)^7-E(15)^8-1/6*E(15)^11-1/6*E(15)^13-1/6*E(15)^14, 1/6*E(15)+1/6*E(15)^2+1/6*E(15)^4-1/2*E(15)^7+1/6*E(15)^8-1/2*E(15)^11-1/2*E(15)^13-1/2*E(15)^14 ], [-1/3*E(15)-1/3*E(15)^2-1/3*E(15)^4+1/3*E(15)^7-1/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, 0,0,-1/3*E(15)-1/3*E(15)^2-1/3*E(15)^4+1/3*E(15)^7-1/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4-1/3*E(15)^7+1/3*E(15)^8-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14, -2/3*E(15)^7-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14,2/3*E(15)^7+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 2/3*E(15)+2/3*E(15)^2+2/3*E(15)^4+1/3*E(15)^7+2/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, E(15)+E(15)^2+E(15)^4+E(15)^8,-2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-1/3*E(15)^7-2/3*E(15)^8-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14, 4/3*E(15)+4/3*E(15)^2+4/3*E(15)^4+2/3*E(15)^7+4/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 4/3*E(15)+4/3*E(15)^2+4/3*E(15)^4+2/3*E(15)^7+4/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, -5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-4/3*E(15)^7-5/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14, -4/3*E(15)-4/3*E(15)^2-4/3*E(15)^4-1/3*E(15)^7-4/3*E(15)^8-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14, 7/3*E(15)+7/3*E(15)^2+7/3*E(15)^4+2*E(15)^7+7/3*E(15)^8+2*E(15)^11+2*E(15)^13+2*E(15)^14, -8/3*E(15)-8/3*E(15)^2-8/3*E(15)^4-5/3*E(15)^7-8/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, -1/3*E(15)-1/3*E(15)^2-1/3*E(15)^4+1/3*E(15)^7-1/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, E(15)+E(15)^2+E(15)^4+2/3*E(15)^7+E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 4/3*E(15)+4/3*E(15)^2+4/3*E(15)^4+1/3*E(15)^7+4/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, -E(15)-E(15)^2-E(15)^4-2/3*E(15)^7-E(15)^8-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14, 7/3*E(15)+7/3*E(15)^2+7/3*E(15)^4+1/3*E(15)^7+7/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14 ]]]; return result;