TII subcells for the Spin(10,3) x PSp(12,R) block of Spin13
#
cell#0 , |C| = 30
special orbit = [7, 1, 1, 1, 1, 1, 1]
special rep = [[3], [1, 1, 1]] , dim = 20
cell rep = phi[[3, 1, 1, 1],[]]+phi[[3],[1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = 10*X+10*X^2
TII subcells:
  tii[17,1] := {0, 2}
  tii[17,2] := {12, 13}
  tii[17,3] := {1, 4}
  tii[17,4] := {14}
  tii[17,5] := {21, 22}
  tii[17,6] := {10, 11}
  tii[17,7] := {18}
  tii[17,8] := {3, 6}
  tii[17,9] := {15}
  tii[17,10] := {23}
  tii[17,11] := {27, 28}
  tii[17,12] := {19, 20}
  tii[17,13] := {26}
  tii[17,14] := {8, 9}
  tii[17,15] := {17}
  tii[17,16] := {25}
  tii[17,17] := {5, 7}
  tii[17,18] := {16}
  tii[17,19] := {24}
  tii[17,20] := {29}

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

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

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

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

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

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

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

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

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

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

cell#11 , |C| = 1
special orbit = [1, 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}