TII subcells for the U(4,4) x GL(4,H) block of GL8
#
cell#0 , |C| = 1
special orbit = [8]
special rep = [8] , dim = 1
cell rep = phi[8]
TII depth = 1
TII multiplicity polynomial = X
TII subcells:
  tii[22,1] := {0}

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

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

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

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