TII subcells for the SO(8,7) x Sp(6,1) block of SO15
#
cell#0 , |C| = 1
special orbit = [15]
special rep = [[7], []] , dim = 1
cell rep = phi[[7],[]]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[40,1] := {0}

cell#1 , |C| = 13
special orbit = [13, 1, 1]
special rep = [[6], [1]] , dim = 7
cell rep = phi[[6, 1],[]]+phi[[6],[1]]
TII depth = 1
TII multiplicity polynomial = X+6*X^2
TII subcells:
  tii[39,1] := {2, 12}
  tii[39,2] := {0, 11}
  tii[39,3] := {1, 10}
  tii[39,4] := {3, 9}
  tii[39,5] := {4, 8}
  tii[39,6] := {5, 7}
  tii[39,7] := {6}

cell#2 , |C| = 35
special orbit = [11, 2, 2]
special rep = [[5, 1], [1]] , dim = 35
cell rep = phi[[5, 1],[1]]
TII depth = 5
TII multiplicity polynomial = 35*X
TII subcells:
  tii[37,1] := {2}
  tii[37,2] := {7}
  tii[37,3] := {12}
  tii[37,4] := {19}
  tii[37,5] := {31}
  tii[37,6] := {34}
  tii[37,7] := {0}
  tii[37,8] := {28}
  tii[37,9] := {1}
  tii[37,10] := {23}
  tii[37,11] := {3}
  tii[37,12] := {18}
  tii[37,13] := {5}
  tii[37,14] := {14}
  tii[37,15] := {10}
  tii[37,16] := {33}
  tii[37,17] := {27}
  tii[37,18] := {4}
  tii[37,19] := {22}
  tii[37,20] := {6}
  tii[37,21] := {17}
  tii[37,22] := {8}
  tii[37,23] := {13}
  tii[37,24] := {32}
  tii[37,25] := {26}
  tii[37,26] := {9}
  tii[37,27] := {21}
  tii[37,28] := {11}
  tii[37,29] := {16}
  tii[37,30] := {30}
  tii[37,31] := {25}
  tii[37,32] := {15}
  tii[37,33] := {20}
  tii[37,34] := {29}
  tii[37,35] := {24}