TII subcells for the SO(9,3) x SO(7,5) block of SO12
#
cell#0 , |C| = 10
special orbit = [7, 1, 1, 1, 1, 1]
special rep = [[], [4, 1, 1]] , dim = 10
cell rep = phi[[],[4, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 10*X
TII subcells:
  tii[22,1] := {0}
  tii[22,2] := {4}
  tii[22,3] := {1}
  tii[22,4] := {7}
  tii[22,5] := {3}
  tii[22,6] := {2}
  tii[22,7] := {5}
  tii[22,8] := {8}
  tii[22,9] := {6}
  tii[22,10] := {9}

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

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

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

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

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

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

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

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

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

cell#10 , |C| = 6
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]]
TII depth = 1
TII multiplicity polynomial = 6*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}

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

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}