TII subcells for the Spin(8,7) x PSp(5,2) block of Spin15
#
cell#0 , |C| = 1
special orbit = [15]
special rep = [[7], []] , dim = 1
cell rep = phi[[7],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[40,1] := {0}

cell#1 , |C| = 13
special orbit = [13, 1, 1]
special rep = [[6], [1]] , dim = 7
cell rep = phi[[6, 1],[]]+phi[[6],[1]]
TII depth = 1
TII multiplicity polynomial = X+6*X^2
TII subcells:
  tii[39,1] := {6, 12}
  tii[39,2] := {4, 11}
  tii[39,3] := {2, 10}
  tii[39,4] := {0, 9}
  tii[39,5] := {1, 8}
  tii[39,6] := {3, 7}
  tii[39,7] := {5}

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

cell#3 , |C| = 35
special orbit = [11, 2, 2]
special rep = [[5, 1], [1]] , dim = 35
cell rep = phi[[5, 1],[1]]
TII depth = 5
TII multiplicity polynomial = 35*X
TII subcells:
  tii[37,1] := {26}
  tii[37,2] := {11}
  tii[37,3] := {2}
  tii[37,4] := {9}
  tii[37,5] := {24}
  tii[37,6] := {34}
  tii[37,7] := {16}
  tii[37,8] := {33}
  tii[37,9] := {12}
  tii[37,10] := {32}
  tii[37,11] := {7}
  tii[37,12] := {30}
  tii[37,13] := {10}
  tii[37,14] := {27}
  tii[37,15] := {17}
  tii[37,16] := {31}
  tii[37,17] := {29}
  tii[37,18] := {6}
  tii[37,19] := {28}
  tii[37,20] := {3}
  tii[37,21] := {19}
  tii[37,22] := {5}
  tii[37,23] := {14}
  tii[37,24] := {25}
  tii[37,25] := {21}
  tii[37,26] := {0}
  tii[37,27] := {15}
  tii[37,28] := {1}
  tii[37,29] := {8}
  tii[37,30] := {23}
  tii[37,31] := {20}
  tii[37,32] := {4}
  tii[37,33] := {13}
  tii[37,34] := {22}
  tii[37,35] := {18}

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

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

cell#6 , |C| = 35
special orbit = [11, 2, 2]
special rep = [[5, 1], [1]] , dim = 35
cell rep = phi[[5, 1],[1]]
TII depth = 5
TII multiplicity polynomial = 35*X
TII subcells:
  tii[37,1] := {34}
  tii[37,2] := {32}
  tii[37,3] := {28}
  tii[37,4] := {22}
  tii[37,5] := {14}
  tii[37,6] := {11}
  tii[37,7] := {33}
  tii[37,8] := {5}
  tii[37,9] := {31}
  tii[37,10] := {10}
  tii[37,11] := {29}
  tii[37,12] := {16}
  tii[37,13] := {26}
  tii[37,14] := {19}
  tii[37,15] := {23}
  tii[37,16] := {0}
  tii[37,17] := {4}
  tii[37,18] := {30}
  tii[37,19] := {9}
  tii[37,20] := {27}
  tii[37,21] := {15}
  tii[37,22] := {24}
  tii[37,23] := {20}
  tii[37,24] := {3}
  tii[37,25] := {7}
  tii[37,26] := {25}
  tii[37,27] := {12}
  tii[37,28] := {21}
  tii[37,29] := {17}
  tii[37,30] := {2}
  tii[37,31] := {6}
  tii[37,32] := {18}
  tii[37,33] := {13}
  tii[37,34] := {1}
  tii[37,35] := {8}

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

cell#8 , |C| = 126
special orbit = [7, 2, 2, 2, 2]
special rep = [[3, 1, 1], [1, 1]] , dim = 126
cell rep = phi[[3, 1, 1],[1, 1]]
TII depth = 4
TII multiplicity polynomial = 126*X
TII subcells:
  tii[24,1] := {124}
  tii[24,2] := {85}
  tii[24,3] := {49}
  tii[24,4] := {116}
  tii[24,5] := {80}
  tii[24,6] := {115}
  tii[24,7] := {36}
  tii[24,8] := {76}
  tii[24,9] := {123}
  tii[24,10] := {112}
  tii[24,11] := {24}
  tii[24,12] := {62}
  tii[24,13] := {64}
  tii[24,14] := {94}
  tii[24,15] := {11}
  tii[24,16] := {30}
  tii[24,17] := {111}
  tii[24,18] := {70}
  tii[24,19] := {22}
  tii[24,20] := {45}
  tii[24,21] := {87}
  tii[24,22] := {41}
  tii[24,23] := {39}
  tii[24,24] := {88}
  tii[24,25] := {71}
  tii[24,26] := {21}
  tii[24,27] := {44}
  tii[24,28] := {60}
  tii[24,29] := {61}
  tii[24,30] := {47}
  tii[24,31] := {35}
  tii[24,32] := {75}
  tii[24,33] := {104}
  tii[24,34] := {17}
  tii[24,35] := {120}
  tii[24,36] := {81}
  tii[24,37] := {33}
  tii[24,38] := {56}
  tii[24,39] := {7}
  tii[24,40] := {107}
  tii[24,41] := {63}
  tii[24,42] := {108}
  tii[24,43] := {42}
  tii[24,44] := {92}
  tii[24,45] := {16}
  tii[24,46] := {59}
  tii[24,47] := {58}
  tii[24,48] := {65}
  tii[24,49] := {38}
  tii[24,50] := {8}
  tii[24,51] := {83}
  tii[24,52] := {84}
  tii[24,53] := {67}
  tii[24,54] := {25}
  tii[24,55] := {74}
  tii[24,56] := {117}
  tii[24,57] := {99}
  tii[24,58] := {52}
  tii[24,59] := {77}
  tii[24,60] := {32}
  tii[24,61] := {102}
  tii[24,62] := {103}
  tii[24,63] := {89}
  tii[24,64] := {55}
  tii[24,65] := {121}
  tii[24,66] := {97}
  tii[24,67] := {125}
  tii[24,68] := {18}
  tii[24,69] := {105}
  tii[24,70] := {34}
  tii[24,71] := {82}
  tii[24,72] := {57}
  tii[24,73] := {122}
  tii[24,74] := {73}
  tii[24,75] := {3}
  tii[24,76] := {101}
  tii[24,77] := {54}
  tii[24,78] := {50}
  tii[24,79] := {9}
  tii[24,80] := {79}
  tii[24,81] := {26}
  tii[24,82] := {118}
  tii[24,83] := {31}
  tii[24,84] := {2}
  tii[24,85] := {98}
  tii[24,86] := {13}
  tii[24,87] := {4}
  tii[24,88] := {0}
  tii[24,89] := {110}
  tii[24,90] := {40}
  tii[24,91] := {43}
  tii[24,92] := {6}
  tii[24,93] := {93}
  tii[24,94] := {20}
  tii[24,95] := {66}
  tii[24,96] := {1}
  tii[24,97] := {109}
  tii[24,98] := {51}
  tii[24,99] := {10}
  tii[24,100] := {12}
  tii[24,101] := {91}
  tii[24,102] := {27}
  tii[24,103] := {14}
  tii[24,104] := {5}
  tii[24,105] := {86}
  tii[24,106] := {19}
  tii[24,107] := {68}
  tii[24,108] := {29}
  tii[24,109] := {119}
  tii[24,110] := {53}
  tii[24,111] := {100}
  tii[24,112] := {78}
  tii[24,113] := {114}
  tii[24,114] := {23}
  tii[24,115] := {72}
  tii[24,116] := {96}
  tii[24,117] := {46}
  tii[24,118] := {28}
  tii[24,119] := {15}
  tii[24,120] := {106}
  tii[24,121] := {37}
  tii[24,122] := {90}
  tii[24,123] := {48}
  tii[24,124] := {113}
  tii[24,125] := {95}
  tii[24,126] := {69}