TII subcells for the Sp(10,R) x SO(8,3) block of Sp10
#
cell#0 , |C| = 1
special orbit = [10]
special rep = [[5], []] , dim = 1
cell rep = phi[[5],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[16,1] := {0}

cell#1 , |C| = 1
special orbit = [10]
special rep = [[5], []] , dim = 1
cell rep = phi[[5],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[16,1] := {0}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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