TII subcells for the Spin(12,3) x PSp(14,R) block of Spin15
#
cell#0 , |C| = 50
special orbit = [7, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[3], [1, 1, 1, 1]] , dim = 35
cell rep = phi[[3, 1, 1, 1, 1],[]]+phi[[3],[1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 20*X+15*X^2
TII subcells:
  tii[22,1] := {0, 2}
  tii[22,2] := {16, 17}
  tii[22,3] := {1, 4}
  tii[22,4] := {18}
  tii[22,5] := {29, 30}
  tii[22,6] := {14, 15}
  tii[22,7] := {24}
  tii[22,8] := {3, 6}
  tii[22,9] := {19}
  tii[22,10] := {31}
  tii[22,11] := {40, 41}
  tii[22,12] := {27, 28}
  tii[22,13] := {37}
  tii[22,14] := {12, 13}
  tii[22,15] := {23}
  tii[22,16] := {35}
  tii[22,17] := {5, 8}
  tii[22,18] := {20}
  tii[22,19] := {32}
  tii[22,20] := {42}
  tii[22,21] := {48, 49}
  tii[22,22] := {38, 39}
  tii[22,23] := {46}
  tii[22,24] := {25, 26}
  tii[22,25] := {36}
  tii[22,26] := {45}
  tii[22,27] := {10, 11}
  tii[22,28] := {22}
  tii[22,29] := {34}
  tii[22,30] := {44}
  tii[22,31] := {7, 9}
  tii[22,32] := {21}
  tii[22,33] := {33}
  tii[22,34] := {43}
  tii[22,35] := {47}

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

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

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

cell#4 , |C| = 36
special orbit = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[2], [1, 1, 1, 1, 1]] , dim = 21
cell rep = phi[[2],[1, 1, 1, 1, 1]]+phi[[],[3, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 6*X+15*X^2
TII subcells:
  tii[11,1] := {3}
  tii[11,2] := {12}
  tii[11,3] := {4, 17}
  tii[11,4] := {16}
  tii[11,5] := {11, 21}
  tii[11,6] := {5, 23}
  tii[11,7] := {20}
  tii[11,8] := {15, 25}
  tii[11,9] := {9, 27}
  tii[11,10] := {6, 30}
  tii[11,11] := {22}
  tii[11,12] := {18, 28}
  tii[11,13] := {13, 31}
  tii[11,14] := {8, 33}
  tii[11,15] := {7, 35}
  tii[11,16] := {19}
  tii[11,17] := {14, 24}
  tii[11,18] := {10, 26}
  tii[11,19] := {2, 29}
  tii[11,20] := {1, 32}
  tii[11,21] := {0, 34}

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

cell#6 , |C| = 35
special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 1, 1, 1, 1]] , dim = 35
cell rep = phi[[1],[2, 1, 1, 1, 1]]
TII depth = 5
TII multiplicity polynomial = 35*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] := {24}
  tii[6,19] := {25}
  tii[6,20] := {29}
  tii[6,21] := {17}
  tii[6,22] := {22}
  tii[6,23] := {23}
  tii[6,24] := {26}
  tii[6,25] := {27}
  tii[6,26] := {30}
  tii[6,27] := {31}
  tii[6,28] := {32}
  tii[6,29] := {33}
  tii[6,30] := {34}
  tii[6,31] := {0}
  tii[6,32] := {2}
  tii[6,33] := {8}
  tii[6,34] := {18}
  tii[6,35] := {28}

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

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

cell#9 , |C| = 28
special orbit = [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1, 1], [1, 1, 1, 1, 1]] , dim = 21
cell rep = phi[[1, 1, 1, 1, 1, 1],[1]]+phi[[1, 1],[1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 14*X+7*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] := {23}
  tii[3,11] := {18, 19}
  tii[3,12] := {22}
  tii[3,13] := {24}
  tii[3,14] := {26}
  tii[3,15] := {27}
  tii[3,16] := {0, 1}
  tii[3,17] := {2, 3}
  tii[3,18] := {6}
  tii[3,19] := {12}
  tii[3,20] := {20}
  tii[3,21] := {25}

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

cell#11 , |C| = 1
special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [1, 1, 1, 1, 1, 1, 1]] , dim = 1
cell rep = phi[[],[1, 1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[1,1] := {0}