TII subcells for the PSp(3,3) x Spin(7,6) block of PSp12
#
cell#0 , |C| = 25
special orbit = [6, 6]
special rep = [[3], [3]] , dim = 20
cell rep = phi[[3, 3],[]]+phi[[3],[3]]
TII depth = 2
TII multiplicity polynomial = 5*X^2+15*X
TII subcells:
  tii[21,1] := {23, 24}
  tii[21,2] := {16}
  tii[21,3] := {8}
  tii[21,4] := {0}
  tii[21,5] := {17, 18}
  tii[21,6] := {11}
  tii[21,7] := {4}
  tii[21,8] := {21, 22}
  tii[21,9] := {19, 20}
  tii[21,10] := {9}
  tii[21,11] := {15}
  tii[21,12] := {1}
  tii[21,13] := {12}
  tii[21,14] := {7}
  tii[21,15] := {6}
  tii[21,16] := {3}
  tii[21,17] := {13, 14}
  tii[21,18] := {10}
  tii[21,19] := {5}
  tii[21,20] := {2}

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

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

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

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

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

cell#6 , |C| = 75
special orbit = [3, 3, 2, 2, 1, 1]
special rep = [[1, 1], [2, 1, 1]] , dim = 45
cell rep = phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]
TII depth = 2
TII multiplicity polynomial = 30*X^2+15*X
TII subcells:
  tii[6,1] := {56}
  tii[6,2] := {48}
  tii[6,3] := {19, 69}
  tii[6,4] := {31, 74}
  tii[6,5] := {55}
  tii[6,6] := {44, 67}
  tii[6,7] := {40}
  tii[6,8] := {13, 62}
  tii[6,9] := {23, 72}
  tii[6,10] := {9, 54}
  tii[6,11] := {46}
  tii[6,12] := {5, 43}
  tii[6,13] := {35, 59}
  tii[6,14] := {17, 66}
  tii[6,15] := {24, 70}
  tii[6,16] := {37}
  tii[6,17] := {26, 50}
  tii[6,18] := {21, 57}
  tii[6,19] := {27}
  tii[6,20] := {41}
  tii[6,21] := {36}
  tii[6,22] := {15, 63}
  tii[6,23] := {49}
  tii[6,24] := {25, 73}
  tii[6,25] := {8, 53}
  tii[6,26] := {33, 68}
  tii[6,27] := {6, 45}
  tii[6,28] := {28}
  tii[6,29] := {12, 61}
  tii[6,30] := {3, 34}
  tii[6,31] := {42}
  tii[6,32] := {11, 58}
  tii[6,33] := {16, 64}
  tii[6,34] := {39, 60}
  tii[6,35] := {1, 29}
  tii[6,36] := {10, 71}
  tii[6,37] := {20}
  tii[6,38] := {7, 52}
  tii[6,39] := {32}
  tii[6,40] := {2, 38}
  tii[6,41] := {30, 51}
  tii[6,42] := {14, 65}
  tii[6,43] := {18}
  tii[6,44] := {4, 47}
  tii[6,45] := {0, 22}

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

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

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

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

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

cell#12 , |C| = 1
special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [1, 1, 1, 1, 1, 1]] , dim = 1
cell rep = phi[[],[1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[1,1] := {0}

cell#13 , |C| = 1
special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [1, 1, 1, 1, 1, 1]] , dim = 1
cell rep = phi[[],[1, 1, 1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[1,1] := {0}