TII subcells for the PSO(11,3) x Spin(8,6) block of PSO14
#
cell#0 , |C| = 20
special orbit = [7, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [4, 1, 1, 1]] , dim = 20
cell rep = phi[[],[4, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 20*X
TII subcells:
  tii[24,1] := {0}
  tii[24,2] := {6}
  tii[24,3] := {1}
  tii[24,4] := {11}
  tii[24,5] := {5}
  tii[24,6] := {2}
  tii[24,7] := {16}
  tii[24,8] := {10}
  tii[24,9] := {4}
  tii[24,10] := {3}
  tii[24,11] := {7}
  tii[24,12] := {13}
  tii[24,13] := {8}
  tii[24,14] := {14}
  tii[24,15] := {18}
  tii[24,16] := {12}
  tii[24,17] := {17}
  tii[24,18] := {9}
  tii[24,19] := {15}
  tii[24,20] := {19}

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

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

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

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

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

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

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

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

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

cell#10 , |C| = 7
special orbit = [2, 2, 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]]
TII depth = 1
TII multiplicity polynomial = 7*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}

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

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