TII subcells for the PSp(5,1) x Spin(7,6) block of PSp12
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cell#0 , |C| = 24
special orbit = [3, 3, 1, 1, 1, 1, 1, 1]
special rep = [[1], [2, 1, 1, 1]] , dim = 24
cell rep = phi[[1],[2, 1, 1, 1]]
TII depth = 4
TII multiplicity polynomial = 24*X
TII subcells:
  tii[5,1] := {8}
  tii[5,2] := {0}
  tii[5,3] := {11}
  tii[5,4] := {15}
  tii[5,5] := {7}
  tii[5,6] := {1}
  tii[5,7] := {14}
  tii[5,8] := {18}
  tii[5,9] := {10}
  tii[5,10] := {19}
  tii[5,11] := {6}
  tii[5,12] := {3}
  tii[5,13] := {16}
  tii[5,14] := {20}
  tii[5,15] := {13}
  tii[5,16] := {22}
  tii[5,17] := {9}
  tii[5,18] := {23}
  tii[5,19] := {5}
  tii[5,20] := {4}
  tii[5,21] := {2}
  tii[5,22] := {12}
  tii[5,23] := {17}
  tii[5,24] := {21}

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

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