TII subcells for the GL(3,H) x U(3,3) block of GL6
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cell#0 , |C| = 5
special orbit = [3, 3]
special rep = [3, 3] , dim = 5
cell rep = phi[3,3]
TII depth = 1
TII multiplicity polynomial = 5*X
TII subcells:
  tii[7,1] := {0}
  tii[7,2] := {4}
  tii[7,3] := {1}
  tii[7,4] := {3}
  tii[7,5] := {2}

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

cell#2 , |C| = 1
special orbit = [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}