TII subcells for the SO(5,4) x Sp(8,R) block of SO9
#
cell#0 , |C| = 1
special orbit = [9]
special rep = [[4], []] , dim = 1
cell rep = phi[[4],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[10,1] := {0}

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

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

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

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

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

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

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

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

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

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

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

cell#12 , |C| = 9
special orbit = [5, 1, 1, 1, 1]
special rep = [[2], [1, 1]] , dim = 6
cell rep = phi[[2],[1, 1]]+phi[[],[3, 1]]
TII depth = 1
TII multiplicity polynomial = 3*X+3*X^2
TII subcells:
  tii[6,1] := {8}
  tii[6,2] := {6}
  tii[6,3] := {3, 7}
  tii[6,4] := {2}
  tii[6,5] := {1, 5}
  tii[6,6] := {0, 4}

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

cell#14 , |C| = 6
special orbit = [3, 3, 3]
special rep = [[1, 1], [2]] , dim = 6
cell rep = phi[[1, 1],[2]]
TII depth = 1
TII multiplicity polynomial = 6*X
TII subcells:
  tii[5,1] := {5}
  tii[5,2] := {1}
  tii[5,3] := {3}
  tii[5,4] := {2}
  tii[5,5] := {4}
  tii[5,6] := {0}

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

cell#16 , |C| = 9
special orbit = [5, 1, 1, 1, 1]
special rep = [[2], [1, 1]] , dim = 6
cell rep = phi[[2],[1, 1]]+phi[[],[3, 1]]
TII depth = 1
TII multiplicity polynomial = 3*X+3*X^2
TII subcells:
  tii[6,1] := {8}
  tii[6,2] := {6}
  tii[6,3] := {3, 7}
  tii[6,4] := {2}
  tii[6,5] := {1, 5}
  tii[6,6] := {0, 4}

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

cell#18 , |C| = 6
special orbit = [3, 3, 3]
special rep = [[1, 1], [2]] , dim = 6
cell rep = phi[[1, 1],[2]]
TII depth = 1
TII multiplicity polynomial = 6*X
TII subcells:
  tii[5,1] := {5}
  tii[5,2] := {1}
  tii[5,3] := {3}
  tii[5,4] := {2}
  tii[5,5] := {4}
  tii[5,6] := {0}

cell#19 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {4}
  tii[4,2] := {7}
  tii[4,3] := {2}
  tii[4,4] := {1}
  tii[4,5] := {5}
  tii[4,6] := {6}
  tii[4,7] := {3}
  tii[4,8] := {0}

cell#20 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {4}
  tii[4,2] := {6}
  tii[4,3] := {2}
  tii[4,4] := {1}
  tii[4,5] := {5}
  tii[4,6] := {7}
  tii[4,7] := {3}
  tii[4,8] := {0}

cell#21 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {4}
  tii[4,2] := {6}
  tii[4,3] := {2}
  tii[4,4] := {1}
  tii[4,5] := {5}
  tii[4,6] := {7}
  tii[4,7] := {3}
  tii[4,8] := {0}

cell#22 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {5}
  tii[4,2] := {7}
  tii[4,3] := {4}
  tii[4,4] := {1}
  tii[4,5] := {6}
  tii[4,6] := {3}
  tii[4,7] := {2}
  tii[4,8] := {0}

cell#23 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {5}
  tii[4,2] := {7}
  tii[4,3] := {4}
  tii[4,4] := {1}
  tii[4,5] := {6}
  tii[4,6] := {3}
  tii[4,7] := {2}
  tii[4,8] := {0}

cell#24 , |C| = 8
special orbit = [3, 2, 2, 1, 1]
special rep = [[1, 1], [1, 1]] , dim = 6
cell rep = phi[[1, 1],[1, 1]]+phi[[],[2, 2]]
TII depth = 1
TII multiplicity polynomial = 4*X+2*X^2
TII subcells:
  tii[3,1] := {3}
  tii[3,2] := {5}
  tii[3,3] := {4, 7}
  tii[3,4] := {0}
  tii[3,5] := {1}
  tii[3,6] := {2, 6}

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

cell#26 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1]
special rep = [[1], [1, 1, 1]] , dim = 4
cell rep = phi[[1],[1, 1, 1]]+phi[[],[2, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X+3*X^2
TII subcells:
  tii[2,1] := {3}
  tii[2,2] := {2, 4}
  tii[2,3] := {1, 6}
  tii[2,4] := {0, 5}

cell#27 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {2}
  tii[4,2] := {5}
  tii[4,3] := {4}
  tii[4,4] := {3}
  tii[4,5] := {6}
  tii[4,6] := {7}
  tii[4,7] := {0}
  tii[4,8] := {1}

cell#28 , |C| = 8
special orbit = [3, 3, 1, 1, 1]
special rep = [[1], [2, 1]] , dim = 8
cell rep = phi[[1],[2, 1]]
TII depth = 2
TII multiplicity polynomial = 8*X
TII subcells:
  tii[4,1] := {2}
  tii[4,2] := {5}
  tii[4,3] := {4}
  tii[4,4] := {3}
  tii[4,5] := {6}
  tii[4,6] := {7}
  tii[4,7] := {0}
  tii[4,8] := {1}

cell#29 , |C| = 8
special orbit = [3, 2, 2, 1, 1]
special rep = [[1, 1], [1, 1]] , dim = 6
cell rep = phi[[1, 1],[1, 1]]+phi[[],[2, 2]]
TII depth = 1
TII multiplicity polynomial = 4*X+2*X^2
TII subcells:
  tii[3,1] := {4}
  tii[3,2] := {5}
  tii[3,3] := {3, 7}
  tii[3,4] := {0}
  tii[3,5] := {2}
  tii[3,6] := {1, 6}

cell#30 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1]
special rep = [[1], [1, 1, 1]] , dim = 4
cell rep = phi[[1],[1, 1, 1]]+phi[[],[2, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X+3*X^2
TII subcells:
  tii[2,1] := {3}
  tii[2,2] := {2, 5}
  tii[2,3] := {1, 4}
  tii[2,4] := {0, 6}

cell#31 , |C| = 8
special orbit = [3, 2, 2, 1, 1]
special rep = [[1, 1], [1, 1]] , dim = 6
cell rep = phi[[1, 1],[1, 1]]+phi[[],[2, 2]]
TII depth = 1
TII multiplicity polynomial = 4*X+2*X^2
TII subcells:
  tii[3,1] := {4}
  tii[3,2] := {5}
  tii[3,3] := {3, 7}
  tii[3,4] := {0}
  tii[3,5] := {2}
  tii[3,6] := {1, 6}

cell#32 , |C| = 7
special orbit = [3, 1, 1, 1, 1, 1, 1]
special rep = [[1], [1, 1, 1]] , dim = 4
cell rep = phi[[1],[1, 1, 1]]+phi[[],[2, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X+3*X^2
TII subcells:
  tii[2,1] := {3}
  tii[2,2] := {2, 5}
  tii[2,3] := {1, 4}
  tii[2,4] := {0, 6}

cell#33 , |C| = 1
special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [1, 1, 1, 1]] , dim = 1
cell rep = phi[[],[1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[1,1] := {0}

cell#34 , |C| = 1
special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[], [1, 1, 1, 1]] , dim = 1
cell rep = phi[[],[1, 1, 1, 1]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[1,1] := {0}