TII subcells for the PSO(13,3) x Spin(9,7) block of PSO16
#
cell#0 , |C| = 35
special orbit = [7, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [4, 1, 1, 1, 1]] , dim = 35
cell rep = phi[[],[4, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 35*X
TII subcells:
  tii[38,1] := {0}
  tii[38,2] := {8}
  tii[38,3] := {1}
  tii[38,4] := {15}
  tii[38,5] := {7}
  tii[38,6] := {2}
  tii[38,7] := {23}
  tii[38,8] := {14}
  tii[38,9] := {6}
  tii[38,10] := {3}
  tii[38,11] := {30}
  tii[38,12] := {22}
  tii[38,13] := {13}
  tii[38,14] := {5}
  tii[38,15] := {4}
  tii[38,16] := {9}
  tii[38,17] := {18}
  tii[38,18] := {10}
  tii[38,19] := {19}
  tii[38,20] := {27}
  tii[38,21] := {17}
  tii[38,22] := {25}
  tii[38,23] := {11}
  tii[38,24] := {20}
  tii[38,25] := {28}
  tii[38,26] := {33}
  tii[38,27] := {26}
  tii[38,28] := {32}
  tii[38,29] := {16}
  tii[38,30] := {24}
  tii[38,31] := {31}
  tii[38,32] := {12}
  tii[38,33] := {21}
  tii[38,34] := {29}
  tii[38,35] := {34}

cell#1 , |C| = 184
special orbit = [5, 3, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [3, 1, 1, 1, 1]] , dim = 120
cell rep = phi[[],[3, 2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]
TII depth = 3
TII multiplicity polynomial = 64*X^2+56*X
TII subcells:
  tii[24,1] := {16, 36}
  tii[24,2] := {10, 47}
  tii[24,3] := {32, 60}
  tii[24,4] := {24, 71}
  tii[24,5] := {42, 85}
  tii[24,6] := {44, 93}
  tii[24,7] := {55, 86}
  tii[24,8] := {45, 98}
  tii[24,9] := {67, 108}
  tii[24,10] := {96, 127}
  tii[24,11] := {69, 113}
  tii[24,12] := {95, 131}
  tii[24,13] := {81, 109}
  tii[24,14] := {70, 117}
  tii[24,15] := {94, 128}
  tii[24,16] := {97, 132}
  tii[24,17] := {116, 144}
  tii[24,18] := {134, 157}
  tii[24,19] := {115, 148}
  tii[24,20] := {133, 161}
  tii[24,21] := {0}
  tii[24,22] := {7, 19}
  tii[24,23] := {1}
  tii[24,24] := {4}
  tii[24,25] := {5}
  tii[24,26] := {23, 59}
  tii[24,27] := {3}
  tii[24,28] := {12}
  tii[24,29] := {13}
  tii[24,30] := {27}
  tii[24,31] := {29}
  tii[24,32] := {54}
  tii[24,33] := {9}
  tii[24,34] := {68, 107}
  tii[24,35] := {26}
  tii[24,36] := {28}
  tii[24,37] := {49}
  tii[24,38] := {51}
  tii[24,39] := {33, 110}
  tii[24,40] := {79}
  tii[24,41] := {73}
  tii[24,42] := {76}
  tii[24,43] := {20, 123}
  tii[24,44] := {104}
  tii[24,45] := {118}
  tii[24,46] := {114, 143}
  tii[24,47] := {22}
  tii[24,48] := {48}
  tii[24,49] := {50}
  tii[24,50] := {74}
  tii[24,51] := {77}
  tii[24,52] := {56, 130}
  tii[24,53] := {105}
  tii[24,54] := {99}
  tii[24,55] := {101}
  tii[24,56] := {40, 139}
  tii[24,57] := {64, 146}
  tii[24,58] := {124}
  tii[24,59] := {57, 158}
  tii[24,60] := {135}
  tii[24,61] := {119}
  tii[24,62] := {121}
  tii[24,63] := {65, 154}
  tii[24,64] := {140}
  tii[24,65] := {37, 163}
  tii[24,66] := {149}
  tii[24,67] := {162}
  tii[24,68] := {43}
  tii[24,69] := {72}
  tii[24,70] := {75}
  tii[24,71] := {100}
  tii[24,72] := {102}
  tii[24,73] := {82, 147}
  tii[24,74] := {125}
  tii[24,75] := {120}
  tii[24,76] := {122}
  tii[24,77] := {66, 155}
  tii[24,78] := {90, 160}
  tii[24,79] := {141}
  tii[24,80] := {83, 169}
  tii[24,81] := {150}
  tii[24,82] := {137}
  tii[24,83] := {138}
  tii[24,84] := {112, 170}
  tii[24,85] := {92, 166}
  tii[24,86] := {156}
  tii[24,87] := {63, 173}
  tii[24,88] := {88, 177}
  tii[24,89] := {164}
  tii[24,90] := {84, 181}
  tii[24,91] := {171}
  tii[24,92] := {152}
  tii[24,93] := {153}
  tii[24,94] := {111, 175}
  tii[24,95] := {167}
  tii[24,96] := {89, 180}
  tii[24,97] := {174}
  tii[24,98] := {61, 183}
  tii[24,99] := {178}
  tii[24,100] := {182}
  tii[24,101] := {2, 15}
  tii[24,102] := {17, 87}
  tii[24,103] := {6, 31}
  tii[24,104] := {8, 80}
  tii[24,105] := {39, 129}
  tii[24,106] := {14, 53}
  tii[24,107] := {34, 145}
  tii[24,108] := {11, 106}
  tii[24,109] := {18, 136}
  tii[24,110] := {91, 159}
  tii[24,111] := {30, 78}
  tii[24,112] := {62, 168}
  tii[24,113] := {25, 126}
  tii[24,114] := {58, 176}
  tii[24,115] := {21, 151}
  tii[24,116] := {35, 172}
  tii[24,117] := {52, 103}
  tii[24,118] := {46, 142}
  tii[24,119] := {41, 165}
  tii[24,120] := {38, 179}

cell#2 , |C| = 21
special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [3, 1, 1, 1, 1, 1]] , dim = 21
cell rep = phi[[],[3, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 21*X
TII subcells:
  tii[23,1] := {16}
  tii[23,2] := {10}
  tii[23,3] := {6}
  tii[23,4] := {3}
  tii[23,5] := {1}
  tii[23,6] := {0}
  tii[23,7] := {19}
  tii[23,8] := {13}
  tii[23,9] := {18}
  tii[23,10] := {8}
  tii[23,11] := {12}
  tii[23,12] := {17}
  tii[23,13] := {4}
  tii[23,14] := {7}
  tii[23,15] := {11}
  tii[23,16] := {15}
  tii[23,17] := {2}
  tii[23,18] := {5}
  tii[23,19] := {9}
  tii[23,20] := {14}
  tii[23,21] := {20}

cell#3 , |C| = 112
special orbit = [3, 3, 3, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 2, 1, 1, 1]] , dim = 112
cell rep = phi[[1],[2, 2, 1, 1, 1]]
TII depth = 4
TII multiplicity polynomial = 112*X
TII subcells:
  tii[11,1] := {18}
  tii[11,2] := {27}
  tii[11,3] := {28}
  tii[11,4] := {41}
  tii[11,5] := {42}
  tii[11,6] := {43}
  tii[11,7] := {54}
  tii[11,8] := {55}
  tii[11,9] := {70}
  tii[11,10] := {56}
  tii[11,11] := {57}
  tii[11,12] := {71}
  tii[11,13] := {72}
  tii[11,14] := {84}
  tii[11,15] := {85}
  tii[11,16] := {95}
  tii[11,17] := {1}
  tii[11,18] := {17}
  tii[11,19] := {4}
  tii[11,20] := {7}
  tii[11,21] := {8}
  tii[11,22] := {40}
  tii[11,23] := {9}
  tii[11,24] := {12}
  tii[11,25] := {14}
  tii[11,26] := {22}
  tii[11,27] := {24}
  tii[11,28] := {39}
  tii[11,29] := {59}
  tii[11,30] := {69}
  tii[11,31] := {16}
  tii[11,32] := {21}
  tii[11,33] := {23}
  tii[11,34] := {35}
  tii[11,35] := {38}
  tii[11,36] := {53}
  tii[11,37] := {48}
  tii[11,38] := {50}
  tii[11,39] := {75}
  tii[11,40] := {76}
  tii[11,41] := {67}
  tii[11,42] := {79}
  tii[11,43] := {89}
  tii[11,44] := {97}
  tii[11,45] := {26}
  tii[11,46] := {33}
  tii[11,47] := {36}
  tii[11,48] := {49}
  tii[11,49] := {51}
  tii[11,50] := {68}
  tii[11,51] := {64}
  tii[11,52] := {66}
  tii[11,53] := {90}
  tii[11,54] := {91}
  tii[11,55] := {83}
  tii[11,56] := {93}
  tii[11,57] := {80}
  tii[11,58] := {81}
  tii[11,59] := {100}
  tii[11,60] := {101}
  tii[11,61] := {94}
  tii[11,62] := {105}
  tii[11,63] := {106}
  tii[11,64] := {103}
  tii[11,65] := {108}
  tii[11,66] := {107}
  tii[11,67] := {110}
  tii[11,68] := {111}
  tii[11,69] := {2}
  tii[11,70] := {3}
  tii[11,71] := {6}
  tii[11,72] := {13}
  tii[11,73] := {15}
  tii[11,74] := {11}
  tii[11,75] := {10}
  tii[11,76] := {25}
  tii[11,77] := {32}
  tii[11,78] := {34}
  tii[11,79] := {37}
  tii[11,80] := {58}
  tii[11,81] := {19}
  tii[11,82] := {20}
  tii[11,83] := {52}
  tii[11,84] := {47}
  tii[11,85] := {62}
  tii[11,86] := {46}
  tii[11,87] := {74}
  tii[11,88] := {63}
  tii[11,89] := {65}
  tii[11,90] := {88}
  tii[11,91] := {29}
  tii[11,92] := {30}
  tii[11,93] := {82}
  tii[11,94] := {96}
  tii[11,95] := {60}
  tii[11,96] := {92}
  tii[11,97] := {61}
  tii[11,98] := {102}
  tii[11,99] := {87}
  tii[11,100] := {86}
  tii[11,101] := {104}
  tii[11,102] := {44}
  tii[11,103] := {45}
  tii[11,104] := {77}
  tii[11,105] := {78}
  tii[11,106] := {98}
  tii[11,107] := {99}
  tii[11,108] := {109}
  tii[11,109] := {0}
  tii[11,110] := {5}
  tii[11,111] := {31}
  tii[11,112] := {73}

cell#4 , |C| = 21
special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [3, 1, 1, 1, 1, 1]] , dim = 21
cell rep = phi[[],[3, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 21*X
TII subcells:
  tii[23,1] := {3}
  tii[23,2] := {12}
  tii[23,3] := {16}
  tii[23,4] := {19}
  tii[23,5] := {20}
  tii[23,6] := {18}
  tii[23,7] := {4}
  tii[23,8] := {11}
  tii[23,9] := {5}
  tii[23,10] := {15}
  tii[23,11] := {9}
  tii[23,12] := {6}
  tii[23,13] := {17}
  tii[23,14] := {13}
  tii[23,15] := {8}
  tii[23,16] := {7}
  tii[23,17] := {14}
  tii[23,18] := {10}
  tii[23,19] := {2}
  tii[23,20] := {1}
  tii[23,21] := {0}

cell#5 , |C| = 21
special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [3, 1, 1, 1, 1, 1]] , dim = 21
cell rep = phi[[],[3, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 21*X
TII subcells:
  tii[23,1] := {0}
  tii[23,2] := {1}
  tii[23,3] := {2}
  tii[23,4] := {5}
  tii[23,5] := {7}
  tii[23,6] := {4}
  tii[23,7] := {3}
  tii[23,8] := {6}
  tii[23,9] := {8}
  tii[23,10] := {10}
  tii[23,11] := {12}
  tii[23,12] := {15}
  tii[23,13] := {13}
  tii[23,14] := {16}
  tii[23,15] := {19}
  tii[23,16] := {20}
  tii[23,17] := {9}
  tii[23,18] := {11}
  tii[23,19] := {14}
  tii[23,20] := {18}
  tii[23,21] := {17}

cell#6 , |C| = 68
special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48
cell rep = phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]
TII depth = 3
TII multiplicity polynomial = 20*X^2+28*X
TII subcells:
  tii[8,1] := {10, 23}
  tii[8,2] := {16, 28}
  tii[8,3] := {22, 34}
  tii[8,4] := {29, 41}
  tii[8,5] := {35, 48}
  tii[8,6] := {3}
  tii[8,7] := {11}
  tii[8,8] := {12}
  tii[8,9] := {17}
  tii[8,10] := {18}
  tii[8,11] := {26}
  tii[8,12] := {24}
  tii[8,13] := {25}
  tii[8,14] := {9, 39}
  tii[8,15] := {32}
  tii[8,16] := {36}
  tii[8,17] := {30}
  tii[8,18] := {31}
  tii[8,19] := {15, 46}
  tii[8,20] := {40}
  tii[8,21] := {8, 50}
  tii[8,22] := {42}
  tii[8,23] := {49}
  tii[8,24] := {37}
  tii[8,25] := {38}
  tii[8,26] := {21, 52}
  tii[8,27] := {47}
  tii[8,28] := {14, 56}
  tii[8,29] := {51}
  tii[8,30] := {7, 60}
  tii[8,31] := {54}
  tii[8,32] := {59}
  tii[8,33] := {44}
  tii[8,34] := {45}
  tii[8,35] := {27, 58}
  tii[8,36] := {53}
  tii[8,37] := {20, 62}
  tii[8,38] := {57}
  tii[8,39] := {13, 65}
  tii[8,40] := {61}
  tii[8,41] := {6, 67}
  tii[8,42] := {63}
  tii[8,43] := {66}
  tii[8,44] := {5, 19}
  tii[8,45] := {4, 33}
  tii[8,46] := {2, 43}
  tii[8,47] := {1, 55}
  tii[8,48] := {0, 64}

cell#7 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [2, 1, 1, 1, 1, 1, 1]] , dim = 7
cell rep = phi[[],[2, 1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 7*X
TII subcells:
  tii[7,1] := {6}
  tii[7,2] := {5}
  tii[7,3] := {4}
  tii[7,4] := {3}
  tii[7,5] := {2}
  tii[7,6] := {1}
  tii[7,7] := {0}

cell#8 , |C| = 68
special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48
cell rep = phi[[],[2, 2, 1, 1, 1, 1]]+phi[[1],[2, 1, 1, 1, 1, 1]]
TII depth = 3
TII multiplicity polynomial = 20*X^2+28*X
TII subcells:
  tii[8,1] := {7, 8}
  tii[8,2] := {12, 13}
  tii[8,3] := {22, 23}
  tii[8,4] := {31, 32}
  tii[8,5] := {21, 42}
  tii[8,6] := {0}
  tii[8,7] := {1}
  tii[8,8] := {2}
  tii[8,9] := {5}
  tii[8,10] := {6}
  tii[8,11] := {11}
  tii[8,12] := {9}
  tii[8,13] := {10}
  tii[8,14] := {24, 25}
  tii[8,15] := {20}
  tii[8,16] := {26}
  tii[8,17] := {17}
  tii[8,18] := {19}
  tii[8,19] := {37, 38}
  tii[8,20] := {30}
  tii[8,21] := {45, 46}
  tii[8,22] := {40}
  tii[8,23] := {50}
  tii[8,24] := {27}
  tii[8,25] := {28}
  tii[8,26] := {47, 48}
  tii[8,27] := {41}
  tii[8,28] := {55, 56}
  tii[8,29] := {51}
  tii[8,30] := {61, 62}
  tii[8,31] := {59}
  tii[8,32] := {64}
  tii[8,33] := {16}
  tii[8,34] := {18}
  tii[8,35] := {36, 57}
  tii[8,36] := {29}
  tii[8,37] := {44, 63}
  tii[8,38] := {39}
  tii[8,39] := {52, 66}
  tii[8,40] := {49}
  tii[8,41] := {43, 67}
  tii[8,42] := {58}
  tii[8,43] := {60}
  tii[8,44] := {3, 4}
  tii[8,45] := {14, 15}
  tii[8,46] := {34, 35}
  tii[8,47] := {53, 54}
  tii[8,48] := {33, 65}

cell#9 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [2, 1, 1, 1, 1, 1, 1]] , dim = 7
cell rep = phi[[],[2, 1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 7*X
TII subcells:
  tii[7,1] := {0}
  tii[7,2] := {1}
  tii[7,3] := {3}
  tii[7,4] := {5}
  tii[7,5] := {6}
  tii[7,6] := {4}
  tii[7,7] := {2}

cell#10 , |C| = 8
special orbit = [2, 2, 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]]
TII depth = 1
TII multiplicity polynomial = 8*X
TII subcells:
  tii[2,1] := {0}
  tii[2,2] := {1}
  tii[2,3] := {2}
  tii[2,4] := {3}
  tii[2,5] := {4}
  tii[2,6] := {5}
  tii[2,7] := {6}
  tii[2,8] := {7}

cell#11 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [2, 1, 1, 1, 1, 1, 1]] , dim = 7
cell rep = phi[[],[2, 1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 7*X
TII subcells:
  tii[7,1] := {0}
  tii[7,2] := {1}
  tii[7,3] := {2}
  tii[7,4] := {3}
  tii[7,5] := {4}
  tii[7,6] := {6}
  tii[7,7] := {5}

cell#12 , |C| = 1
special orbit = [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}