TII subcells for the Sp(7,1) x SO(9,8) block of Sp16
#
cell#0 , |C| = 48
special orbit = [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 1, 1, 1, 1, 1]] , dim = 48
cell rep = phi[[1],[2, 1, 1, 1, 1, 1]]
TII depth = 6
TII multiplicity polynomial = 48*X
TII subcells:
  tii[6,1] := {12}
  tii[6,2] := {0}
  tii[6,3] := {17}
  tii[6,4] := {23}
  tii[6,5] := {11}
  tii[6,6] := {1}
  tii[6,7] := {22}
  tii[6,8] := {28}
  tii[6,9] := {16}
  tii[6,10] := {31}
  tii[6,11] := {10}
  tii[6,12] := {3}
  tii[6,13] := {26}
  tii[6,14] := {32}
  tii[6,15] := {21}
  tii[6,16] := {35}
  tii[6,17] := {15}
  tii[6,18] := {37}
  tii[6,19] := {9}
  tii[6,20] := {4}
  tii[6,21] := {30}
  tii[6,22] := {36}
  tii[6,23] := {25}
  tii[6,24] := {38}
  tii[6,25] := {20}
  tii[6,26] := {41}
  tii[6,27] := {14}
  tii[6,28] := {43}
  tii[6,29] := {8}
  tii[6,30] := {5}
  tii[6,31] := {34}
  tii[6,32] := {39}
  tii[6,33] := {29}
  tii[6,34] := {42}
  tii[6,35] := {24}
  tii[6,36] := {44}
  tii[6,37] := {19}
  tii[6,38] := {46}
  tii[6,39] := {13}
  tii[6,40] := {47}
  tii[6,41] := {7}
  tii[6,42] := {6}
  tii[6,43] := {2}
  tii[6,44] := {18}
  tii[6,45] := {27}
  tii[6,46] := {33}
  tii[6,47] := {40}
  tii[6,48] := {45}

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

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