TII subcells for the SO(7,6) x Sp(3,3) block of SO13
#
cell#0 , |C| = 1
special orbit = [13]
special rep = [[6], []] , dim = 1
cell rep = phi[[6],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[26,1] := {0}

cell#1 , |C| = 11
special orbit = [11, 1, 1]
special rep = [[5], [1]] , dim = 6
cell rep = phi[[5, 1],[]]+phi[[5],[1]]
TII depth = 1
TII multiplicity polynomial = 5*X^2+X
TII subcells:
  tii[25,1] := {9, 10}
  tii[25,2] := {7, 8}
  tii[25,3] := {5, 6}
  tii[25,4] := {3, 4}
  tii[25,5] := {1, 2}
  tii[25,6] := {0}

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

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

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

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

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

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

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

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

cell#10 , |C| = 185
special orbit = [5, 3, 3, 1, 1]
special rep = [[2, 1], [2, 1]] , dim = 80
cell rep = phi[[2, 2, 1],[1]]+phi[[2, 1, 1],[2]]+phi[[2, 2],[1, 1]]+phi[[2, 1],[2, 1]]
TII depth = 3
TII multiplicity polynomial = 25*X+30*X^2+25*X^4
TII subcells:
  tii[13,1] := {132, 133, 183, 184}
  tii[13,2] := {157, 158}
  tii[13,3] := {29, 152}
  tii[13,4] := {100, 101, 181, 182}
  tii[13,5] := {47, 48, 165, 166}
  tii[13,6] := {130, 131}
  tii[13,7] := {91}
  tii[13,8] := {124}
  tii[13,9] := {134, 135, 175, 176}
  tii[13,10] := {118, 119}
  tii[13,11] := {102, 103, 167, 168}
  tii[13,12] := {31}
  tii[13,13] := {142, 143}
  tii[13,14] := {62}
  tii[13,15] := {150, 151}
  tii[13,16] := {125}
  tii[13,17] := {37, 38, 159, 160}
  tii[13,18] := {77, 78, 173, 174}
  tii[13,19] := {104, 105}
  tii[13,20] := {140, 141}
  tii[13,21] := {17, 18, 169, 170}
  tii[13,22] := {11, 122}
  tii[13,23] := {108, 109, 179, 180}
  tii[13,24] := {39, 40, 153, 154}
  tii[13,25] := {23, 24, 146, 147}
  tii[13,26] := {58}
  tii[13,27] := {30, 92}
  tii[13,28] := {69, 70}
  tii[13,29] := {81, 82, 171, 172}
  tii[13,30] := {94}
  tii[13,31] := {61}
  tii[13,32] := {112, 113}
  tii[13,33] := {96, 97}
  tii[13,34] := {32}
  tii[13,35] := {45, 46, 120, 121}
  tii[13,36] := {15}
  tii[13,37] := {128, 129}
  tii[13,38] := {87, 88}
  tii[13,39] := {63}
  tii[13,40] := {36}
  tii[13,41] := {5, 6, 161, 162}
  tii[13,42] := {57, 123}
  tii[13,43] := {75, 76, 177, 178}
  tii[13,44] := {19, 20, 136, 137}
  tii[13,45] := {41, 42}
  tii[13,46] := {93}
  tii[13,47] := {51, 52, 163, 164}
  tii[13,48] := {83, 84}
  tii[13,49] := {73, 74, 148, 149}
  tii[13,50] := {7, 8, 106, 107}
  tii[13,51] := {65, 66}
  tii[13,52] := {13}
  tii[13,53] := {60}
  tii[13,54] := {116, 117}
  tii[13,55] := {98, 99}
  tii[13,56] := {27, 28, 144, 145}
  tii[13,57] := {3}
  tii[13,58] := {35}
  tii[13,59] := {89, 90}
  tii[13,60] := {64}
  tii[13,61] := {43, 44}
  tii[13,62] := {14}
  tii[13,63] := {85, 86}
  tii[13,64] := {95}
  tii[13,65] := {67, 68, 138, 139}
  tii[13,66] := {110, 111}
  tii[13,67] := {21, 22, 126, 127}
  tii[13,68] := {12, 59}
  tii[13,69] := {79, 80}
  tii[13,70] := {34}
  tii[13,71] := {53, 54, 155, 156}
  tii[13,72] := {16}
  tii[13,73] := {1, 2, 71, 72}
  tii[13,74] := {33}
  tii[13,75] := {49, 50}
  tii[13,76] := {9, 10, 114, 115}
  tii[13,77] := {4}
  tii[13,78] := {55, 56}
  tii[13,79] := {25, 26}
  tii[13,80] := {0}

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

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

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