TII subcells for the Sp(4,2) x SO(7,6) block of Sp12
#
cell#0 , |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] := {29}
  tii[15,2] := {15}
  tii[15,3] := {0}
  tii[15,4] := {37}
  tii[15,5] := {40}
  tii[15,6] := {19}
  tii[15,7] := {44}
  tii[15,8] := {8}
  tii[15,9] := {42}
  tii[15,10] := {38}
  tii[15,11] := {16}
  tii[15,12] := {43}
  tii[15,13] := {28}
  tii[15,14] := {1}
  tii[15,15] := {25}
  tii[15,16] := {36}
  tii[15,17] := {14}
  tii[15,18] := {5}
  tii[15,19] := {17}
  tii[15,20] := {7}
  tii[15,21] := {20}
  tii[15,22] := {34}
  tii[15,23] := {11}
  tii[15,24] := {41}
  tii[15,25] := {12}
  tii[15,26] := {24}
  tii[15,27] := {4}
  tii[15,28] := {13}
  tii[15,29] := {35}
  tii[15,30] := {26}
  tii[15,31] := {30}
  tii[15,32] := {21}
  tii[15,33] := {22}
  tii[15,34] := {31}
  tii[15,35] := {33}
  tii[15,36] := {10}
  tii[15,37] := {39}
  tii[15,38] := {18}
  tii[15,39] := {9}
  tii[15,40] := {32}
  tii[15,41] := {6}
  tii[15,42] := {27}
  tii[15,43] := {2}
  tii[15,44] := {23}
  tii[15,45] := {3}

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

cell#2 , |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] := {24}
  tii[8,3] := {28}
  tii[8,4] := {20}
  tii[8,5] := {7}
  tii[8,6] := {13}
  tii[8,7] := {15}
  tii[8,8] := {23}
  tii[8,9] := {10}
  tii[8,10] := {12}
  tii[8,11] := {18}
  tii[8,12] := {14}
  tii[8,13] := {19}
  tii[8,14] := {22}
  tii[8,15] := {26}
  tii[8,16] := {16}
  tii[8,17] := {29}
  tii[8,18] := {21}
  tii[8,19] := {3}
  tii[8,20] := {8}
  tii[8,21] := {1}
  tii[8,22] := {4}
  tii[8,23] := {9}
  tii[8,24] := {2}
  tii[8,25] := {17}
  tii[8,26] := {27}
  tii[8,27] := {5}
  tii[8,28] := {6}
  tii[8,29] := {11}
  tii[8,30] := {0}

cell#3 , |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] := {17}
  tii[5,2] := {22}
  tii[5,3] := {13}
  tii[5,4] := {9}
  tii[5,5] := {18}
  tii[5,6] := {21}
  tii[5,7] := {10}
  tii[5,8] := {7}
  tii[5,9] := {16}
  tii[5,10] := {4}
  tii[5,11] := {20}
  tii[5,12] := {23}
  tii[5,13] := {8}
  tii[5,14] := {5}
  tii[5,15] := {11}
  tii[5,16] := {3}
  tii[5,17] := {15}
  tii[5,18] := {1}
  tii[5,19] := {19}
  tii[5,20] := {14}
  tii[5,21] := {12}
  tii[5,22] := {6}
  tii[5,23] := {2}
  tii[5,24] := {0}

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

cell#5 , |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] := {16}
  tii[5,2] := {12}
  tii[5,3] := {20}
  tii[5,4] := {23}
  tii[5,5] := {15}
  tii[5,6] := {13}
  tii[5,7] := {17}
  tii[5,8] := {21}
  tii[5,9] := {8}
  tii[5,10] := {19}
  tii[5,11] := {7}
  tii[5,12] := {4}
  tii[5,13] := {9}
  tii[5,14] := {18}
  tii[5,15] := {5}
  tii[5,16] := {10}
  tii[5,17] := {3}
  tii[5,18] := {6}
  tii[5,19] := {1}
  tii[5,20] := {0}
  tii[5,21] := {14}
  tii[5,22] := {22}
  tii[5,23] := {11}
  tii[5,24] := {2}

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

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

cell#8 , |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}