TII subcells for the SL(4,H) x PU(4,4) block of SL8
#
cell#0 , |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] := {0}
  tii[15,2] := {12}
  tii[15,3] := {5}
  tii[15,4] := {13}
  tii[15,5] := {1}
  tii[15,6] := {4}
  tii[15,7] := {9}
  tii[15,8] := {11}
  tii[15,9] := {8}
  tii[15,10] := {3}
  tii[15,11] := {2}
  tii[15,12] := {6}
  tii[15,13] := {10}
  tii[15,14] := {7}

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

cell#2 , |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] := {5}
  tii[5,2] := {11}
  tii[5,3] := {7}
  tii[5,4] := {12}
  tii[5,5] := {1}
  tii[5,6] := {6}
  tii[5,7] := {10}
  tii[5,8] := {3}
  tii[5,9] := {9}
  tii[5,10] := {4}
  tii[5,11] := {13}
  tii[5,12] := {8}
  tii[5,13] := {2}
  tii[5,14] := {0}

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

cell#4 , |C| = 1
special orbit = [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}