TII subcells for the Spin(14,3) x PSp(16,R) block of Spin17 # cell#0 , |C| = 77 special orbit = [7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[3], [1, 1, 1, 1, 1]] , dim = 56 cell rep = phi[[3, 1, 1, 1, 1, 1],[]]+phi[[3],[1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = 35*X+21*X^2 TII subcells: tii[29,1] := {0, 2} tii[29,2] := {20, 21} tii[29,3] := {1, 4} tii[29,4] := {22} tii[29,5] := {37, 38} tii[29,6] := {18, 19} tii[29,7] := {30} tii[29,8] := {3, 6} tii[29,9] := {23} tii[29,10] := {39} tii[29,11] := {53, 54} tii[29,12] := {35, 36} tii[29,13] := {48} tii[29,14] := {16, 17} tii[29,15] := {29} tii[29,16] := {45} tii[29,17] := {5, 8} tii[29,18] := {24} tii[29,19] := {40} tii[29,20] := {55} tii[29,21] := {68, 69} tii[29,22] := {51, 52} tii[29,23] := {63} tii[29,24] := {33, 34} tii[29,25] := {47} tii[29,26] := {61} tii[29,27] := {14, 15} tii[29,28] := {28} tii[29,29] := {44} tii[29,30] := {59} tii[29,31] := {7, 10} tii[29,32] := {25} tii[29,33] := {41} tii[29,34] := {56} tii[29,35] := {66} tii[29,36] := {75, 76} tii[29,37] := {64, 65} tii[29,38] := {73} tii[29,39] := {49, 50} tii[29,40] := {62} tii[29,41] := {72} tii[29,42] := {31, 32} tii[29,43] := {46} tii[29,44] := {60} tii[29,45] := {71} tii[29,46] := {12, 13} tii[29,47] := {27} tii[29,48] := {43} tii[29,49] := {58} tii[29,50] := {70} tii[29,51] := {9, 11} tii[29,52] := {26} tii[29,53] := {42} tii[29,54] := {57} tii[29,55] := {67} tii[29,56] := {74} cell#1 , |C| = 260 special orbit = [5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[2], [2, 1, 1, 1, 1]] , dim = 140 cell rep = phi[[2],[2, 1, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]] TII depth = 5 TII multiplicity polynomial = 20*X+120*X^2 TII subcells: tii[16,1] := {8} tii[16,2] := {4, 32} tii[16,3] := {18, 43} tii[16,4] := {19} tii[16,5] := {28} tii[16,6] := {14, 58} tii[16,7] := {20, 62} tii[16,8] := {35, 70} tii[16,9] := {29, 81} tii[16,10] := {11, 99} tii[16,11] := {61, 100} tii[16,12] := {88, 128} tii[16,13] := {37} tii[16,14] := {53} tii[16,15] := {30, 87} tii[16,16] := {38, 92} tii[16,17] := {63, 102} tii[16,18] := {84} tii[16,19] := {55, 112} tii[16,20] := {26, 129} tii[16,21] := {49, 123} tii[16,22] := {91, 130} tii[16,23] := {39, 146} tii[16,24] := {119, 154} tii[16,25] := {83, 135} tii[16,26] := {50, 155} tii[16,27] := {122, 156} tii[16,28] := {23, 177} tii[16,29] := {145, 178} tii[16,30] := {165, 199} tii[16,31] := {64} tii[16,32] := {82} tii[16,33] := {56, 118} tii[16,34] := {65, 125} tii[16,35] := {93, 132} tii[16,36] := {116} tii[16,37] := {85, 139} tii[16,38] := {51, 157} tii[16,39] := {77, 150} tii[16,40] := {124, 158} tii[16,41] := {66, 171} tii[16,42] := {147, 180} tii[16,43] := {141} tii[16,44] := {115, 161} tii[16,45] := {110, 174} tii[16,46] := {79, 181} tii[16,47] := {149, 182} tii[16,48] := {47, 200} tii[16,49] := {74, 192} tii[16,50] := {170, 201} tii[16,51] := {67, 210} tii[16,52] := {187, 218} tii[16,53] := {140, 185} tii[16,54] := {109, 204} tii[16,55] := {173, 205} tii[16,56] := {75, 219} tii[16,57] := {191, 220} tii[16,58] := {44, 232} tii[16,59] := {209, 233} tii[16,60] := {226, 245} tii[16,61] := {94} tii[16,62] := {113} tii[16,63] := {86, 144} tii[16,64] := {95, 152} tii[16,65] := {126, 160} tii[16,66] := {143} tii[16,67] := {117, 164} tii[16,68] := {80, 183} tii[16,69] := {108, 176} tii[16,70] := {151, 184} tii[16,71] := {96, 194} tii[16,72] := {172, 203} tii[16,73] := {168} tii[16,74] := {142, 186} tii[16,75] := {111, 206} tii[16,76] := {138, 197} tii[16,77] := {175, 207} tii[16,78] := {76, 221} tii[16,79] := {105, 214} tii[16,80] := {193, 222} tii[16,81] := {97, 229} tii[16,82] := {211, 235} tii[16,83] := {190} tii[16,84] := {167, 208} tii[16,85] := {163, 216} tii[16,86] := {137, 223} tii[16,87] := {196, 224} tii[16,88] := {134, 231} tii[16,89] := {107, 236} tii[16,90] := {213, 237} tii[16,91] := {73, 246} tii[16,92] := {103, 243} tii[16,93] := {228, 247} tii[16,94] := {98, 251} tii[16,95] := {240, 253} tii[16,96] := {189, 225} tii[16,97] := {162, 238} tii[16,98] := {215, 239} tii[16,99] := {133, 248} tii[16,100] := {230, 249} tii[16,101] := {104, 254} tii[16,102] := {242, 255} tii[16,103] := {71, 257} tii[16,104] := {250, 258} tii[16,105] := {256, 259} tii[16,106] := {2} tii[16,107] := {0, 7} tii[16,108] := {13} tii[16,109] := {1, 17} tii[16,110] := {9, 36} tii[16,111] := {3, 42} tii[16,112] := {54} tii[16,113] := {6, 33} tii[16,114] := {25, 90} tii[16,115] := {5, 69} tii[16,116] := {21, 120} tii[16,117] := {10, 127} tii[16,118] := {114} tii[16,119] := {16, 59} tii[16,120] := {78, 148} tii[16,121] := {15, 101} tii[16,122] := {46, 169} tii[16,123] := {12, 153} tii[16,124] := {40, 188} tii[16,125] := {22, 198} tii[16,126] := {166} tii[16,127] := {34, 89} tii[16,128] := {136, 195} tii[16,129] := {106, 212} tii[16,130] := {31, 131} tii[16,131] := {72, 227} tii[16,132] := {27, 179} tii[16,133] := {24, 217} tii[16,134] := {68, 241} tii[16,135] := {41, 244} tii[16,136] := {60, 121} tii[16,137] := {57, 159} tii[16,138] := {52, 202} tii[16,139] := {48, 234} tii[16,140] := {45, 252} cell#2 , |C| = 168 special orbit = [3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1, 1], [2, 1, 1, 1, 1]] , dim = 140 cell rep = phi[[1, 1, 1, 1, 1, 1],[2]]+phi[[1, 1],[2, 1, 1, 1, 1]] TII depth = 4 TII multiplicity polynomial = 112*X+28*X^2 TII subcells: tii[7,1] := {16, 17} tii[7,2] := {25, 26} tii[7,3] := {31} tii[7,4] := {43} tii[7,5] := {34, 35} tii[7,6] := {47} tii[7,7] := {38, 39} tii[7,8] := {45} tii[7,9] := {58} tii[7,10] := {59} tii[7,11] := {49, 50} tii[7,12] := {73} tii[7,13] := {63} tii[7,14] := {74} tii[7,15] := {89} tii[7,16] := {65, 66} tii[7,17] := {81} tii[7,18] := {98} tii[7,19] := {51, 52} tii[7,20] := {60} tii[7,21] := {76} tii[7,22] := {67, 68} tii[7,23] := {78} tii[7,24] := {92} tii[7,25] := {82} tii[7,26] := {93} tii[7,27] := {109} tii[7,28] := {96} tii[7,29] := {84, 85} tii[7,30] := {110} tii[7,31] := {111} tii[7,32] := {100} tii[7,33] := {125} tii[7,34] := {117} tii[7,35] := {126} tii[7,36] := {141} tii[7,37] := {102, 103} tii[7,38] := {119} tii[7,39] := {135} tii[7,40] := {148} tii[7,41] := {69, 70} tii[7,42] := {79} tii[7,43] := {95} tii[7,44] := {86, 87} tii[7,45] := {97} tii[7,46] := {112} tii[7,47] := {101} tii[7,48] := {113} tii[7,49] := {128} tii[7,50] := {115} tii[7,51] := {104, 105} tii[7,52] := {131} tii[7,53] := {120} tii[7,54] := {132} tii[7,55] := {144} tii[7,56] := {136} tii[7,57] := {145} tii[7,58] := {155} tii[7,59] := {133} tii[7,60] := {121, 122} tii[7,61] := {146} tii[7,62] := {147} tii[7,63] := {137} tii[7,64] := {156} tii[7,65] := {157} tii[7,66] := {150} tii[7,67] := {162} tii[7,68] := {159} tii[7,69] := {163} tii[7,70] := {166} tii[7,71] := {138, 139} tii[7,72] := {151} tii[7,73] := {160} tii[7,74] := {165} tii[7,75] := {167} tii[7,76] := {2, 3} tii[7,77] := {6, 7} tii[7,78] := {4, 5} tii[7,79] := {20} tii[7,80] := {11, 12} tii[7,81] := {30} tii[7,82] := {13} tii[7,83] := {22} tii[7,84] := {9, 10} tii[7,85] := {44} tii[7,86] := {21} tii[7,87] := {18, 19} tii[7,88] := {55} tii[7,89] := {56} tii[7,90] := {33} tii[7,91] := {72} tii[7,92] := {42} tii[7,93] := {61} tii[7,94] := {14, 15} tii[7,95] := {77} tii[7,96] := {32} tii[7,97] := {27, 28} tii[7,98] := {90} tii[7,99] := {91} tii[7,100] := {57} tii[7,101] := {106} tii[7,102] := {48} tii[7,103] := {107} tii[7,104] := {80} tii[7,105] := {124} tii[7,106] := {88} tii[7,107] := {116} tii[7,108] := {23, 24} tii[7,109] := {114} tii[7,110] := {46} tii[7,111] := {40, 41} tii[7,112] := {129} tii[7,113] := {130} tii[7,114] := {75} tii[7,115] := {142} tii[7,116] := {143} tii[7,117] := {64} tii[7,118] := {108} tii[7,119] := {152} tii[7,120] := {153} tii[7,121] := {99} tii[7,122] := {161} tii[7,123] := {134} tii[7,124] := {140} tii[7,125] := {158} tii[7,126] := {36, 37} tii[7,127] := {62} tii[7,128] := {53, 54} tii[7,129] := {94} tii[7,130] := {83} tii[7,131] := {127} tii[7,132] := {118} tii[7,133] := {154} tii[7,134] := {149} tii[7,135] := {164} tii[7,136] := {0, 1} tii[7,137] := {8} tii[7,138] := {29} tii[7,139] := {71} tii[7,140] := {123} cell#3 , |C| = 35 special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[2], [1, 1, 1, 1, 1, 1]] , dim = 28 cell rep = phi[[2, 1, 1, 1, 1, 1, 1],[]]+phi[[2],[1, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = 21*X+7*X^2 TII subcells: tii[12,1] := {33, 34} tii[12,2] := {25, 26} tii[12,3] := {31} tii[12,4] := {17, 18} tii[12,5] := {23} tii[12,6] := {30} tii[12,7] := {11, 12} tii[12,8] := {16} tii[12,9] := {22} tii[12,10] := {29} tii[12,11] := {6, 7} tii[12,12] := {10} tii[12,13] := {15} tii[12,14] := {21} tii[12,15] := {28} tii[12,16] := {2, 3} tii[12,17] := {5} tii[12,18] := {9} tii[12,19] := {14} tii[12,20] := {20} tii[12,21] := {27} tii[12,22] := {0, 1} tii[12,23] := {4} tii[12,24] := {8} tii[12,25] := {13} tii[12,26] := {19} tii[12,27] := {24} tii[12,28] := {32} cell#4 , |C| = 49 special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[2], [1, 1, 1, 1, 1, 1]] , dim = 28 cell rep = phi[[2],[1, 1, 1, 1, 1, 1]]+phi[[],[3, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = 7*X+21*X^2 TII subcells: tii[12,1] := {3} tii[12,2] := {14} tii[12,3] := {4, 20} tii[12,4] := {19} tii[12,5] := {13, 25} tii[12,6] := {5, 29} tii[12,7] := {24} tii[12,8] := {18, 30} tii[12,9] := {12, 32} tii[12,10] := {6, 35} tii[12,11] := {28} tii[12,12] := {23, 34} tii[12,13] := {17, 37} tii[12,14] := {10, 40} tii[12,15] := {7, 43} tii[12,16] := {31} tii[12,17] := {26, 38} tii[12,18] := {21, 41} tii[12,19] := {15, 44} tii[12,20] := {9, 46} tii[12,21] := {8, 48} tii[12,22] := {27} tii[12,23] := {22, 33} tii[12,24] := {16, 36} tii[12,25] := {11, 39} tii[12,26] := {2, 42} tii[12,27] := {1, 45} tii[12,28] := {0, 47} cell#5 , |C| = 48 special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48 cell rep = phi[[1],[2, 1, 1, 1, 1, 1]] TII depth = 6 TII multiplicity polynomial = 48*X TII subcells: tii[6,1] := {11} tii[6,2] := {17} tii[6,3] := {16} tii[6,4] := {10} tii[6,5] := {22} tii[6,6] := {26} tii[6,7] := {21} tii[6,8] := {15} tii[6,9] := {27} tii[6,10] := {9} tii[6,11] := {30} tii[6,12] := {32} tii[6,13] := {25} tii[6,14] := {20} tii[6,15] := {31} tii[6,16] := {14} tii[6,17] := {34} tii[6,18] := {8} tii[6,19] := {36} tii[6,20] := {39} tii[6,21] := {29} tii[6,22] := {24} tii[6,23] := {35} tii[6,24] := {19} tii[6,25] := {37} tii[6,26] := {13} tii[6,27] := {40} tii[6,28] := {7} tii[6,29] := {42} tii[6,30] := {44} tii[6,31] := {33} tii[6,32] := {28} tii[6,33] := {38} tii[6,34] := {23} tii[6,35] := {41} tii[6,36] := {18} tii[6,37] := {43} tii[6,38] := {12} tii[6,39] := {45} tii[6,40] := {6} tii[6,41] := {46} tii[6,42] := {47} tii[6,43] := {5} tii[6,44] := {4} tii[6,45] := {3} tii[6,46] := {2} tii[6,47] := {1} tii[6,48] := {0} cell#6 , |C| = 48 special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48 cell rep = phi[[1],[2, 1, 1, 1, 1, 1]] TII depth = 6 TII multiplicity polynomial = 48*X TII subcells: tii[6,1] := {1} tii[6,2] := {3} tii[6,3] := {4} tii[6,4] := {5} tii[6,5] := {6} tii[6,6] := {9} tii[6,7] := {7} tii[6,8] := {10} tii[6,9] := {11} tii[6,10] := {13} tii[6,11] := {14} tii[6,12] := {19} tii[6,13] := {12} tii[6,14] := {15} tii[6,15] := {16} tii[6,16] := {20} tii[6,17] := {21} tii[6,18] := {25} tii[6,19] := {26} tii[6,20] := {32} tii[6,21] := {17} tii[6,22] := {22} tii[6,23] := {23} tii[6,24] := {27} tii[6,25] := {28} tii[6,26] := {33} tii[6,27] := {34} tii[6,28] := {37} tii[6,29] := {38} tii[6,30] := {42} tii[6,31] := {24} tii[6,32] := {29} tii[6,33] := {30} tii[6,34] := {35} tii[6,35] := {36} tii[6,36] := {39} tii[6,37] := {40} tii[6,38] := {43} tii[6,39] := {44} tii[6,40] := {45} tii[6,41] := {46} tii[6,42] := {47} tii[6,43] := {0} tii[6,44] := {2} tii[6,45] := {8} tii[6,46] := {18} tii[6,47] := {31} tii[6,48] := {41} cell#7 , |C| = 15 special orbit = [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1], [1, 1, 1, 1, 1, 1, 1]] , dim = 8 cell rep = phi[[1],[1, 1, 1, 1, 1, 1, 1]]+phi[[],[2, 1, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = X+7*X^2 TII subcells: tii[2,1] := {7} tii[2,2] := {6, 8} tii[2,3] := {5, 9} tii[2,4] := {4, 10} tii[2,5] := {3, 11} tii[2,6] := {2, 12} tii[2,7] := {1, 13} tii[2,8] := {0, 14} cell#8 , |C| = 48 special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48 cell rep = phi[[1],[2, 1, 1, 1, 1, 1]] TII depth = 6 TII multiplicity polynomial = 48*X TII subcells: tii[6,1] := {1} tii[6,2] := {3} tii[6,3] := {4} tii[6,4] := {5} tii[6,5] := {6} tii[6,6] := {9} tii[6,7] := {7} tii[6,8] := {10} tii[6,9] := {11} tii[6,10] := {14} tii[6,11] := {15} tii[6,12] := {23} tii[6,13] := {13} tii[6,14] := {18} tii[6,15] := {19} tii[6,16] := {26} tii[6,17] := {27} tii[6,18] := {33} tii[6,19] := {34} tii[6,20] := {40} tii[6,21] := {20} tii[6,22] := {28} tii[6,23] := {29} tii[6,24] := {35} tii[6,25] := {36} tii[6,26] := {41} tii[6,27] := {42} tii[6,28] := {45} tii[6,29] := {46} tii[6,30] := {47} tii[6,31] := {12} tii[6,32] := {16} tii[6,33] := {17} tii[6,34] := {24} tii[6,35] := {25} tii[6,36] := {31} tii[6,37] := {32} tii[6,38] := {37} tii[6,39] := {38} tii[6,40] := {30} tii[6,41] := {44} tii[6,42] := {43} tii[6,43] := {0} tii[6,44] := {2} tii[6,45] := {8} tii[6,46] := {22} tii[6,47] := {39} tii[6,48] := {21} cell#9 , |C| = 36 special orbit = [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1, 1], [1, 1, 1, 1, 1, 1]] , dim = 28 cell rep = phi[[1, 1, 1, 1, 1, 1, 1],[1]]+phi[[1, 1],[1, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = 20*X+8*X^2 TII subcells: tii[3,1] := {4, 5} tii[3,2] := {7, 8} tii[3,3] := {9} tii[3,4] := {10, 11} tii[3,5] := {13} tii[3,6] := {16} tii[3,7] := {14, 15} tii[3,8] := {17} tii[3,9] := {21} tii[3,10] := {25} tii[3,11] := {18, 19} tii[3,12] := {22} tii[3,13] := {26} tii[3,14] := {29} tii[3,15] := {31} tii[3,16] := {23, 24} tii[3,17] := {27} tii[3,18] := {30} tii[3,19] := {32} tii[3,20] := {34} tii[3,21] := {35} tii[3,22] := {0, 1} tii[3,23] := {2, 3} tii[3,24] := {6} tii[3,25] := {12} tii[3,26] := {20} tii[3,27] := {28} tii[3,28] := {33} cell#10 , |C| = 15 special orbit = [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[1], [1, 1, 1, 1, 1, 1, 1]] , dim = 8 cell rep = phi[[1],[1, 1, 1, 1, 1, 1, 1]]+phi[[],[2, 1, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = X+7*X^2 TII subcells: tii[2,1] := {0} tii[2,2] := {1, 2} tii[2,3] := {3, 4} tii[2,4] := {6, 7} tii[2,5] := {9, 10} tii[2,6] := {11, 12} tii[2,7] := {8, 14} tii[2,8] := {5, 13} cell#11 , |C| = 1 special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [[], [1, 1, 1, 1, 1, 1, 1, 1]] , dim = 1 cell rep = phi[[],[1, 1, 1, 1, 1, 1, 1, 1]] TII depth = 1 TII multiplicity polynomial = X TII subcells: tii[1,1] := {0}