complex nilpotent orbits for connected split real group with Lie algebra 'e8(R)' i: orbit number H: semisimple element BC Levi: Bala-Carter Levi Cent: identity component of Cent(SL(2)) Z(Cent^0): order of center of derived group of id. comp. of Centralizer A(O): orders of conj. classes in component group of centralizer #RF(O): number of real forms of O C_2: conjugacy classes in Cent(SL(2))^2 with square 1 i H diagram dim BC Levi Cent Z(Cent^0) A(O) #RF(O) C_2 0 [0,0,0,0,0,0,0,0] [0,0,0,0,0,0,0,0] 0 8T1 E8 1 [1] 1 3 1 [2,3,4,6,5,4,3,2] [0,0,0,0,0,0,0,1] 58 A1+7T1 E7 2 [1] 1 4 2 [4,5,7,10,8,6,4,2] [1,0,0,0,0,0,0,0] 92 2A1+6T1 B6 2 [1] 1 5 3 [4,6,8,12,10,8,6,3] [0,0,0,0,0,0,1,0] 112 3A1+5T1 A1+F4 2 [1] 1 6 4 [4,6,8,12,10,8,6,4] [0,0,0,0,0,0,0,2] 114 A2+6T1 E6 3 [1,2] 2 3 5 [5,8,10,15,12,9,6,3] [0,1,0,0,0,0,0,0] 128 4A1+4T1 C4 2 [1] 1 5 6 [6,8,11,16,13,10,7,4] [1,0,0,0,0,0,0,1] 136 A1+A2+5T1 A5 6 [1,2] 2 4 7 [6,9,12,18,15,12,8,4] [0,0,0,0,0,1,0,0] 146 2A1+A2+4T1 A1+B3 2 [1] 2 5 8 [8,11,15,22,18,14,10,6] [1,0,0,0,0,0,0,2] 148 A3+5T1 B5 2 [1] 1 4 9 [7,10,14,20,16,12,8,4] [0,0,1,0,0,0,0,0] 154 3A1+A2+3T1 A1+G2 2 [1] 2 4 10 [8,10,14,20,16,12,8,4] [2,0,0,0,0,0,0,0] 156 2A2+4T1 2G2 1 [1,2] 3 4 11 [8,11,15,22,18,14,10,5] [1,0,0,0,0,0,1,0] 162 A1+2A2+3T1 A1+G2 2 [1] 1 4 12 [8,12,16,24,20,16,11,6] [0,0,0,0,0,1,0,1] 164 A1+A3+4T1 A1+B3 4 [1] 1 6 13 [8,12,16,24,20,16,12,6] [0,0,0,0,0,0,2,0] 166 D4+4T1 D4 4 [1,2,3] 2 5 14 [12,18,24,36,30,24,18,10] [0,0,0,0,0,0,2,2] 168 D4+4T1 F4 1 [1] 1 3 15 [8,12,16,24,20,15,10,5] [0,0,0,0,1,0,0,0] 168 2A1+2A2+2T1 B2 2 [1] 1 3 16 [9,13,18,26,21,16,11,6] [0,0,1,0,0,0,0,1] 172 2A1+A3+3T1 A1+B2 4 [1] 1 6 17 [9,14,18,27,22,17,12,6] [0,1,0,0,0,0,1,0] 176 A1+D4+3T1 3A1 8 [1,2,3] 2 8 18 [10,14,19,28,23,18,12,6] [1,0,0,0,0,1,0,0] 178 A2+A3+3T1 B2+T1 2 [1,2] 3 4 19 [12,16,22,32,26,20,14,8] [2,0,0,0,0,0,0,2] 180 A4+4T1 A4 5 [1,2] 2 3 20 [10,15,20,30,24,18,12,6] [0,0,0,1,0,0,0,0] 182 A1+A2+A3+2T1 2A1 2 [1] 2 4 21 [13,20,26,39,32,25,18,10] [0,1,0,0,0,0,1,2] 184 A1+D4+3T1 C3 2 [1] 1 4 22 [10,16,20,30,24,18,12,6] [0,2,0,0,0,0,0,0] 184 A2+D4+2T1 A2 1 [1,2] 3 2 23 [12,17,23,34,28,22,15,8] [1,0,0,0,0,1,0,1] 188 A1+A4+3T1 A2+T1 3 [1,2] 2 4 24 [12,17,23,34,28,21,14,7] [1,0,0,0,1,0,0,0] 188 2A3+2T1 C2 2 [1] 1 3 25 [14,20,27,40,33,26,18,10] [1,0,0,0,0,1,0,2] 190 D5+3T1 A3 4 [1,2] 2 3 26 [12,18,24,36,29,22,15,8] [0,0,0,1,0,0,0,1] 192 2A1+A4+2T1 A1+T1 2 [1,2] 3 3 27 [12,18,24,36,30,24,16,8] [0,0,0,0,0,2,0,0] 194 A2+A4+2T1 2A1 2 [1] 2 3 28 [16,22,30,44,36,28,19,10] [2,0,0,0,0,1,0,1] 196 A5+3T1 A1+G2 2 [1] 1 4 29 [14,21,28,42,34,26,18,10] [0,0,0,1,0,0,0,2] 196 A1+D5+2T1 2A1 2 [1] 2 4 30 [13,19,26,38,31,24,16,8] [0,0,1,0,0,1,0,0] 196 A1+A2+A4+T1 A1 2 [1] 1 2 31 [16,22,30,44,36,28,20,10] [2,0,0,0,0,0,2,0] 198 E6+2T1 G2 1 [1,2] 2 2 32 [14,22,28,42,34,26,18,10] [0,2,0,0,0,0,0,2] 198 A2+D4+2T1 A2 3 [1,2] 3 2 33 [20,28,38,56,46,36,26,14] [2,0,0,0,0,0,2,2] 200 D5+3T1 B3 2 [1] 1 3 34 [14,21,28,42,34,26,18,9] [0,0,0,1,0,0,1,0] 200 A3+A4+T1 A1 2 [1] 1 2 35 [16,23,31,46,37,28,19,10] [1,0,0,1,0,0,0,1] 202 A1+A5+2T1 2A1 4 [1] 1 4 36 [15,22,30,44,36,28,19,10] [0,0,1,0,0,1,0,1] 202 A2+D5+T1 A1 2 [1] 1 2 37 [16,24,32,47,38,29,20,10] [0,1,1,0,0,0,1,0] 204 D6+2T1 2A1 4 [1,2] 2 4 38 [16,23,31,46,38,29,20,10] [1,0,0,0,1,0,1,0] 204 A1+E6+T1 A1 2 [1,2] 2 2 39 [16,24,32,48,39,30,20,10] [0,0,0,1,0,1,0,0] 206 E7+T1 A1 2 [1,2,3] 2 2 40 [20,29,39,58,48,37,26,14] [1,0,0,0,1,0,1,2] 208 A1+D5+2T1 2A1 4 [1] 1 4 41 [16,24,32,48,40,30,20,10] [0,0,0,0,2,0,0,0] 208 E8 e 1 [1,2,2,3,4,5,6] 3 1 42 [20,28,38,56,46,36,24,12] [2,0,0,0,0,2,0,0] 210 A6+2T1 2A1 2 [1] 2 3 43 [20,30,40,59,48,37,26,14] [0,1,1,0,0,0,1,2] 210 D6+2T1 2A1 4 [1,2] 2 4 44 [20,30,40,60,49,38,26,14] [0,0,0,1,0,1,0,2] 212 E7+T1 A1 2 [1,2] 2 2 45 [20,29,39,58,47,36,24,12] [1,0,0,1,0,1,0,0] 212 A1+A6+T1 A1 2 [1] 1 2 46 [24,34,46,68,56,44,30,16] [2,0,0,0,0,2,0,2] 214 E6+2T1 A2 3 [1,2] 2 2 47 [20,30,40,60,50,38,26,14] [0,0,0,0,2,0,0,2] 214 A2+D5+T1 T1 1 [1,2] 3 2 48 [32,46,62,92,76,60,42,22] [2,0,0,0,0,2,2,2] 216 E6+2T1 G2 1 [1] 1 2 49 [28,40,54,79,64,49,34,18] [2,1,1,0,0,0,1,2] 216 D6+2T1 B2 2 [1] 1 3 50 [22,32,43,64,52,40,27,14] [1,0,0,1,0,1,0,1] 216 D7+T1 T1 1 [1,2] 2 2 51 [24,35,47,70,57,44,30,16] [1,0,0,1,0,1,0,2] 218 A1+E6+T1 T1 1 [1,2] 2 2 52 [24,35,47,70,57,44,30,15] [1,0,0,1,0,1,1,0] 218 A7+T1 A1 2 [1] 1 2 53 [28,40,54,80,65,50,34,18] [2,0,0,1,0,1,0,2] 220 E7+T1 A1 2 [1,2] 2 2 54 [24,36,48,72,58,44,30,16] [0,0,0,2,0,0,0,2] 220 E8 e 1 [1,2,3] 2 1 55 [32,47,63,94,77,60,42,22] [1,0,0,1,0,1,2,2] 222 A1+E6+T1 A1 2 [1] 1 2 56 [28,40,54,80,66,50,34,18] [2,0,0,0,2,0,0,2] 222 D7+T1 T1 1 [1,2] 3 2 57 [32,48,64,95,78,60,42,22] [0,1,1,0,1,0,2,2] 224 E7+T1 A1 2 [1] 1 2 58 [28,42,56,84,68,52,36,18] [0,0,0,2,0,0,2,0] 224 E8 e 1 [1,2,3] 2 1 59 [36,52,70,103,84,64,43,22] [2,1,1,0,1,1,0,1] 226 D7+T1 A1 2 [1] 1 2 60 [32,48,64,96,78,60,42,22] [0,0,0,2,0,0,2,2] 226 E8 e 1 [1,2,3] 2 1 61 [40,58,78,115,94,72,50,26] [2,1,1,0,1,0,2,2] 228 E7+T1 A1 2 [1] 1 2 62 [36,52,70,104,84,64,44,22] [2,0,0,2,0,0,2,0] 228 E8 e 1 [1,2] 2 1 63 [40,58,78,116,94,72,50,26] [2,0,0,2,0,0,2,2] 230 E8 e 1 [1,2] 2 1 64 [52,76,102,151,124,96,66,34] [2,1,1,0,1,2,2,2] 232 E7+T1 A1 2 [1] 1 2 65 [44,64,86,128,104,80,54,28] [2,0,0,2,0,2,0,2] 232 E8 e 1 [1,2] 2 1 66 [52,76,102,152,124,96,66,34] [2,0,0,2,0,2,2,2] 234 E8 e 1 [1,2] 2 1 67 [60,88,118,174,142,108,74,38] [2,2,2,0,2,0,2,2] 236 E8 e 1 [1] 1 1 68 [72,106,142,210,172,132,90,46] [2,2,2,0,2,2,2,2] 238 E8 e 1 [1] 1 1 69 [92,136,182,270,220,168,114,58] [2,2,2,2,2,2,2,2] 240 E8 e 1 [1] 1 1