TII subcells for the U(7,2) x GL(9,R) block of GL9 # cell#0 , |C| = 70 special orbit = [5, 1, 1, 1, 1] special rep = [5, 1, 1, 1, 1] , dim = 70 cell rep = phi[5,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 70*X TII subcells: tii[19,1] := {0} tii[19,2] := {22} tii[19,3] := {1} tii[19,4] := {15} tii[19,5] := {3} tii[19,6] := {46} tii[19,7] := {25} tii[19,8] := {35} tii[19,9] := {26} tii[19,10] := {2} tii[19,11] := {16} tii[19,12] := {5} tii[19,13] := {41} tii[19,14] := {19} tii[19,15] := {8} tii[19,16] := {62} tii[19,17] := {48} tii[19,18] := {54} tii[19,19] := {49} tii[19,20] := {28} tii[19,21] := {36} tii[19,22] := {29} tii[19,23] := {53} tii[19,24] := {37} tii[19,25] := {30} tii[19,26] := {4} tii[19,27] := {17} tii[19,28] := {7} tii[19,29] := {42} tii[19,30] := {20} tii[19,31] := {10} tii[19,32] := {59} tii[19,33] := {44} tii[19,34] := {23} tii[19,35] := {12} tii[19,36] := {69} tii[19,37] := {63} tii[19,38] := {66} tii[19,39] := {64} tii[19,40] := {50} tii[19,41] := {57} tii[19,42] := {51} tii[19,43] := {67} tii[19,44] := {58} tii[19,45] := {52} tii[19,46] := {31} tii[19,47] := {38} tii[19,48] := {32} tii[19,49] := {55} tii[19,50] := {39} tii[19,51] := {33} tii[19,52] := {65} tii[19,53] := {56} tii[19,54] := {40} tii[19,55] := {34} tii[19,56] := {6} tii[19,57] := {18} tii[19,58] := {9} tii[19,59] := {43} tii[19,60] := {21} tii[19,61] := {11} tii[19,62] := {60} tii[19,63] := {45} tii[19,64] := {24} tii[19,65] := {13} tii[19,66] := {68} tii[19,67] := {61} tii[19,68] := {47} tii[19,69] := {27} tii[19,70] := {14} cell#1 , |C| = 56 special orbit = [4, 1, 1, 1, 1, 1] special rep = [4, 1, 1, 1, 1, 1] , dim = 56 cell rep = phi[4,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 56*X TII subcells: tii[13,1] := {2} tii[13,2] := {11} tii[13,3] := {0} tii[13,4] := {6} tii[13,5] := {24} tii[13,6] := {12} tii[13,7] := {16} tii[13,8] := {1} tii[13,9] := {7} tii[13,10] := {20} tii[13,11] := {37} tii[13,12] := {25} tii[13,13] := {29} tii[13,14] := {13} tii[13,15] := {17} tii[13,16] := {28} tii[13,17] := {3} tii[13,18] := {8} tii[13,19] := {21} tii[13,20] := {34} tii[13,21] := {48} tii[13,22] := {38} tii[13,23] := {41} tii[13,24] := {26} tii[13,25] := {31} tii[13,26] := {42} tii[13,27] := {14} tii[13,28] := {18} tii[13,29] := {30} tii[13,30] := {40} tii[13,31] := {4} tii[13,32] := {9} tii[13,33] := {22} tii[13,34] := {35} tii[13,35] := {46} tii[13,36] := {55} tii[13,37] := {49} tii[13,38] := {51} tii[13,39] := {39} tii[13,40] := {44} tii[13,41] := {52} tii[13,42] := {27} tii[13,43] := {33} tii[13,44] := {45} tii[13,45] := {53} tii[13,46] := {15} tii[13,47] := {19} tii[13,48] := {32} tii[13,49] := {43} tii[13,50] := {50} tii[13,51] := {5} tii[13,52] := {10} tii[13,53] := {23} tii[13,54] := {36} tii[13,55] := {47} tii[13,56] := {54} cell#2 , |C| = 120 special orbit = [3, 3, 1, 1, 1] special rep = [3, 3, 1, 1, 1] , dim = 120 cell rep = phi[3,3,1,1,1] TII depth = 2 TII multiplicity polynomial = 120*X TII subcells: tii[10,1] := {25} tii[10,2] := {46} tii[10,3] := {59} tii[10,4] := {68} tii[10,5] := {45} tii[10,6] := {26} tii[10,7] := {73} tii[10,8] := {85} tii[10,9] := {92} tii[10,10] := {93} tii[10,11] := {72} tii[10,12] := {50} tii[10,13] := {86} tii[10,14] := {63} tii[10,15] := {107} tii[10,16] := {91} tii[10,17] := {71} tii[10,18] := {70} tii[10,19] := {48} tii[10,20] := {29} tii[10,21] := {101} tii[10,22] := {104} tii[10,23] := {112} tii[10,24] := {113} tii[10,25] := {100} tii[10,26] := {80} tii[10,27] := {105} tii[10,28] := {89} tii[10,29] := {117} tii[10,30] := {118} tii[10,31] := {111} tii[10,32] := {98} tii[10,33] := {99} tii[10,34] := {114} tii[10,35] := {103} tii[10,36] := {79} tii[10,37] := {56} tii[10,38] := {106} tii[10,39] := {90} tii[10,40] := {67} tii[10,41] := {119} tii[10,42] := {116} tii[10,43] := {109} tii[10,44] := {110} tii[10,45] := {97} tii[10,46] := {77} tii[10,47] := {96} tii[10,48] := {76} tii[10,49] := {54} tii[10,50] := {32} tii[10,51] := {4} tii[10,52] := {12} tii[10,53] := {35} tii[10,54] := {6} tii[10,55] := {16} tii[10,56] := {5} tii[10,57] := {28} tii[10,58] := {69} tii[10,59] := {19} tii[10,60] := {27} tii[10,61] := {60} tii[10,62] := {37} tii[10,63] := {13} tii[10,64] := {38} tii[10,65] := {8} tii[10,66] := {36} tii[10,67] := {18} tii[10,68] := {7} tii[10,69] := {51} tii[10,70] := {108} tii[10,71] := {40} tii[10,72] := {94} tii[10,73] := {52} tii[10,74] := {62} tii[10,75] := {31} tii[10,76] := {75} tii[10,77] := {22} tii[10,78] := {87} tii[10,79] := {49} tii[10,80] := {64} tii[10,81] := {74} tii[10,82] := {30} tii[10,83] := {14} tii[10,84] := {42} tii[10,85] := {41} tii[10,86] := {10} tii[10,87] := {61} tii[10,88] := {39} tii[10,89] := {21} tii[10,90] := {9} tii[10,91] := {81} tii[10,92] := {65} tii[10,93] := {83} tii[10,94] := {88} tii[10,95] := {57} tii[10,96] := {43} tii[10,97] := {84} tii[10,98] := {102} tii[10,99] := {58} tii[10,100] := {66} tii[10,101] := {34} tii[10,102] := {24} tii[10,103] := {78} tii[10,104] := {115} tii[10,105] := {55} tii[10,106] := {33} tii[10,107] := {82} tii[10,108] := {15} tii[10,109] := {44} tii[10,110] := {11} tii[10,111] := {0} tii[10,112] := {17} tii[10,113] := {1} tii[10,114] := {47} tii[10,115] := {20} tii[10,116] := {2} tii[10,117] := {95} tii[10,118] := {53} tii[10,119] := {23} tii[10,120] := {3} cell#3 , |C| = 105 special orbit = [3, 2, 1, 1, 1, 1] special rep = [3, 2, 1, 1, 1, 1] , dim = 105 cell rep = phi[3,2,1,1,1,1] TII depth = 3 TII multiplicity polynomial = 105*X TII subcells: tii[7,1] := {2} tii[7,2] := {7} tii[7,3] := {6} tii[7,4] := {15} tii[7,5] := {12} tii[7,6] := {20} tii[7,7] := {25} tii[7,8] := {14} tii[7,9] := {13} tii[7,10] := {29} tii[7,11] := {23} tii[7,12] := {35} tii[7,13] := {30} tii[7,14] := {42} tii[7,15] := {28} tii[7,16] := {43} tii[7,17] := {36} tii[7,18] := {61} tii[7,19] := {41} tii[7,20] := {27} tii[7,21] := {24} tii[7,22] := {49} tii[7,23] := {39} tii[7,24] := {56} tii[7,25] := {65} tii[7,26] := {50} tii[7,27] := {48} tii[7,28] := {66} tii[7,29] := {57} tii[7,30] := {68} tii[7,31] := {81} tii[7,32] := {82} tii[7,33] := {64} tii[7,34] := {47} tii[7,35] := {67} tii[7,36] := {58} tii[7,37] := {93} tii[7,38] := {80} tii[7,39] := {63} tii[7,40] := {46} tii[7,41] := {40} tii[7,42] := {74} tii[7,43] := {60} tii[7,44] := {76} tii[7,45] := {88} tii[7,46] := {75} tii[7,47] := {73} tii[7,48] := {89} tii[7,49] := {77} tii[7,50] := {91} tii[7,51] := {97} tii[7,52] := {87} tii[7,53] := {98} tii[7,54] := {72} tii[7,55] := {90} tii[7,56] := {78} tii[7,57] := {99} tii[7,58] := {102} tii[7,59] := {103} tii[7,60] := {96} tii[7,61] := {100} tii[7,62] := {86} tii[7,63] := {71} tii[7,64] := {92} tii[7,65] := {79} tii[7,66] := {104} tii[7,67] := {101} tii[7,68] := {95} tii[7,69] := {85} tii[7,70] := {70} tii[7,71] := {0} tii[7,72] := {1} tii[7,73] := {5} tii[7,74] := {3} tii[7,75] := {10} tii[7,76] := {4} tii[7,77] := {16} tii[7,78] := {9} tii[7,79] := {26} tii[7,80] := {8} tii[7,81] := {21} tii[7,82] := {11} tii[7,83] := {45} tii[7,84] := {18} tii[7,85] := {62} tii[7,86] := {19} tii[7,87] := {44} tii[7,88] := {17} tii[7,89] := {37} tii[7,90] := {22} tii[7,91] := {83} tii[7,92] := {32} tii[7,93] := {94} tii[7,94] := {84} tii[7,95] := {33} tii[7,96] := {69} tii[7,97] := {34} tii[7,98] := {59} tii[7,99] := {31} tii[7,100] := {38} tii[7,101] := {52} tii[7,102] := {53} tii[7,103] := {54} tii[7,104] := {55} tii[7,105] := {51} cell#4 , |C| = 27 special orbit = [2, 2, 1, 1, 1, 1, 1] special rep = [2, 2, 1, 1, 1, 1, 1] , dim = 27 cell rep = phi[2,2,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 27*X TII subcells: tii[3,1] := {1} tii[3,2] := {3} tii[3,3] := {4} tii[3,4] := {5} tii[3,5] := {7} tii[3,6] := {9} tii[3,7] := {8} tii[3,8] := {10} tii[3,9] := {13} tii[3,10] := {16} tii[3,11] := {11} tii[3,12] := {14} tii[3,13] := {17} tii[3,14] := {20} tii[3,15] := {22} tii[3,16] := {15} tii[3,17] := {18} tii[3,18] := {21} tii[3,19] := {23} tii[3,20] := {25} tii[3,21] := {26} tii[3,22] := {0} tii[3,23] := {2} tii[3,24] := {6} tii[3,25] := {12} tii[3,26] := {19} tii[3,27] := {24} cell#5 , |C| = 56 special orbit = [4, 1, 1, 1, 1, 1] special rep = [4, 1, 1, 1, 1, 1] , dim = 56 cell rep = phi[4,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 56*X TII subcells: tii[13,1] := {55} tii[13,2] := {48} tii[13,3] := {51} tii[13,4] := {49} tii[13,5] := {37} tii[13,6] := {42} tii[13,7] := {38} tii[13,8] := {52} tii[13,9] := {43} tii[13,10] := {39} tii[13,11] := {24} tii[13,12] := {31} tii[13,13] := {25} tii[13,14] := {44} tii[13,15] := {32} tii[13,16] := {26} tii[13,17] := {53} tii[13,18] := {45} tii[13,19] := {33} tii[13,20] := {27} tii[13,21] := {11} tii[13,22] := {16} tii[13,23] := {12} tii[13,24] := {28} tii[13,25] := {17} tii[13,26] := {13} tii[13,27] := {40} tii[13,28] := {29} tii[13,29] := {18} tii[13,30] := {14} tii[13,31] := {50} tii[13,32] := {41} tii[13,33] := {30} tii[13,34] := {19} tii[13,35] := {15} tii[13,36] := {0} tii[13,37] := {6} tii[13,38] := {1} tii[13,39] := {20} tii[13,40] := {7} tii[13,41] := {2} tii[13,42] := {34} tii[13,43] := {21} tii[13,44] := {8} tii[13,45] := {3} tii[13,46] := {46} tii[13,47] := {35} tii[13,48] := {22} tii[13,49] := {9} tii[13,50] := {4} tii[13,51] := {54} tii[13,52] := {47} tii[13,53] := {36} tii[13,54] := {23} tii[13,55] := {10} tii[13,56] := {5} cell#6 , |C| = 28 special orbit = [3, 1, 1, 1, 1, 1, 1] special rep = [3, 1, 1, 1, 1, 1, 1] , dim = 28 cell rep = phi[3,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 28*X TII subcells: tii[6,1] := {27} tii[6,2] := {20} tii[6,3] := {22} tii[6,4] := {14} tii[6,5] := {16} tii[6,6] := {23} tii[6,7] := {9} tii[6,8] := {11} tii[6,9] := {17} tii[6,10] := {24} tii[6,11] := {5} tii[6,12] := {7} tii[6,13] := {12} tii[6,14] := {18} tii[6,15] := {25} tii[6,16] := {2} tii[6,17] := {3} tii[6,18] := {6} tii[6,19] := {10} tii[6,20] := {15} tii[6,21] := {21} tii[6,22] := {0} tii[6,23] := {1} tii[6,24] := {4} tii[6,25] := {8} tii[6,26] := {13} tii[6,27] := {19} tii[6,28] := {26} cell#7 , |C| = 105 special orbit = [3, 2, 1, 1, 1, 1] special rep = [3, 2, 1, 1, 1, 1] , dim = 105 cell rep = phi[3,2,1,1,1,1] TII depth = 3 TII multiplicity polynomial = 105*X TII subcells: tii[7,1] := {71} tii[7,2] := {76} tii[7,3] := {87} tii[7,4] := {88} tii[7,5] := {70} tii[7,6] := {49} tii[7,7] := {77} tii[7,8] := {58} tii[7,9] := {97} tii[7,10] := {98} tii[7,11] := {86} tii[7,12] := {68} tii[7,13] := {69} tii[7,14] := {89} tii[7,15] := {73} tii[7,16] := {48} tii[7,17] := {30} tii[7,18] := {78} tii[7,19] := {59} tii[7,20] := {39} tii[7,21] := {102} tii[7,22] := {103} tii[7,23] := {96} tii[7,24] := {84} tii[7,25] := {100} tii[7,26] := {85} tii[7,27] := {92} tii[7,28] := {66} tii[7,29] := {46} tii[7,30] := {67} tii[7,31] := {91} tii[7,32] := {47} tii[7,33] := {74} tii[7,34] := {53} tii[7,35] := {29} tii[7,36] := {17} tii[7,37] := {79} tii[7,38] := {60} tii[7,39] := {40} tii[7,40] := {24} tii[7,41] := {104} tii[7,42] := {93} tii[7,43] := {101} tii[7,44] := {94} tii[7,45] := {81} tii[7,46] := {95} tii[7,47] := {62} tii[7,48] := {82} tii[7,49] := {64} tii[7,50] := {83} tii[7,51] := {61} tii[7,52] := {41} tii[7,53] := {65} tii[7,54] := {25} tii[7,55] := {44} tii[7,56] := {27} tii[7,57] := {63} tii[7,58] := {56} tii[7,59] := {43} tii[7,60] := {36} tii[7,61] := {26} tii[7,62] := {21} tii[7,63] := {11} tii[7,64] := {15} tii[7,65] := {7} tii[7,66] := {35} tii[7,67] := {20} tii[7,68] := {10} tii[7,69] := {4} tii[7,70] := {1} tii[7,71] := {50} tii[7,72] := {37} tii[7,73] := {52} tii[7,74] := {57} tii[7,75] := {31} tii[7,76] := {22} tii[7,77] := {54} tii[7,78] := {72} tii[7,79] := {33} tii[7,80] := {38} tii[7,81] := {18} tii[7,82] := {12} tii[7,83] := {55} tii[7,84] := {90} tii[7,85] := {34} tii[7,86] := {51} tii[7,87] := {19} tii[7,88] := {23} tii[7,89] := {9} tii[7,90] := {6} tii[7,91] := {45} tii[7,92] := {99} tii[7,93] := {28} tii[7,94] := {16} tii[7,95] := {75} tii[7,96] := {8} tii[7,97] := {32} tii[7,98] := {3} tii[7,99] := {13} tii[7,100] := {2} tii[7,101] := {80} tii[7,102] := {42} tii[7,103] := {14} tii[7,104] := {5} tii[7,105] := {0} cell#8 , |C| = 27 special orbit = [2, 2, 1, 1, 1, 1, 1] special rep = [2, 2, 1, 1, 1, 1, 1] , dim = 27 cell rep = phi[2,2,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 27*X TII subcells: tii[3,1] := {26} tii[3,2] := {25} tii[3,3] := {22} tii[3,4] := {23} tii[3,5] := {21} tii[3,6] := {17} tii[3,7] := {19} tii[3,8] := {16} tii[3,9] := {12} tii[3,10] := {9} tii[3,11] := {18} tii[3,12] := {15} tii[3,13] := {11} tii[3,14] := {8} tii[3,15] := {5} tii[3,16] := {14} tii[3,17] := {10} tii[3,18] := {7} tii[3,19] := {4} tii[3,20] := {2} tii[3,21] := {1} tii[3,22] := {24} tii[3,23] := {20} tii[3,24] := {13} tii[3,25] := {6} tii[3,26] := {3} tii[3,27] := {0} cell#9 , |C| = 28 special orbit = [3, 1, 1, 1, 1, 1, 1] special rep = [3, 1, 1, 1, 1, 1, 1] , dim = 28 cell rep = phi[3,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 28*X TII subcells: tii[6,1] := {1} tii[6,2] := {3} tii[6,3] := {6} tii[6,4] := {5} tii[6,5] := {12} tii[6,6] := {7} tii[6,7] := {14} tii[6,8] := {19} tii[6,9] := {13} tii[6,10] := {8} tii[6,11] := {20} tii[6,12] := {24} tii[6,13] := {21} tii[6,14] := {15} tii[6,15] := {9} tii[6,16] := {25} tii[6,17] := {27} tii[6,18] := {26} tii[6,19] := {22} tii[6,20] := {16} tii[6,21] := {10} tii[6,22] := {17} tii[6,23] := {23} tii[6,24] := {18} tii[6,25] := {11} tii[6,26] := {4} tii[6,27] := {2} tii[6,28] := {0} cell#10 , |C| = 27 special orbit = [2, 2, 1, 1, 1, 1, 1] special rep = [2, 2, 1, 1, 1, 1, 1] , dim = 27 cell rep = phi[2,2,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 27*X TII subcells: tii[3,1] := {11} tii[3,2] := {16} tii[3,3] := {10} tii[3,4] := {20} tii[3,5] := {15} tii[3,6] := {9} tii[3,7] := {23} tii[3,8] := {19} tii[3,9] := {14} tii[3,10] := {8} tii[3,11] := {25} tii[3,12] := {22} tii[3,13] := {18} tii[3,14] := {13} tii[3,15] := {7} tii[3,16] := {26} tii[3,17] := {24} tii[3,18] := {21} tii[3,19] := {17} tii[3,20] := {12} tii[3,21] := {6} tii[3,22] := {1} tii[3,23] := {2} tii[3,24] := {3} tii[3,25] := {4} tii[3,26] := {5} tii[3,27] := {0} cell#11 , |C| = 8 special orbit = [2, 1, 1, 1, 1, 1, 1, 1] special rep = [2, 1, 1, 1, 1, 1, 1, 1] , dim = 8 cell rep = phi[2,1,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 8*X TII subcells: tii[2,1] := {5} tii[2,2] := {7} tii[2,3] := {6} tii[2,4] := {4} tii[2,5] := {3} tii[2,6] := {2} tii[2,7] := {1} tii[2,8] := {0} cell#12 , |C| = 8 special orbit = [2, 1, 1, 1, 1, 1, 1, 1] special rep = [2, 1, 1, 1, 1, 1, 1, 1] , dim = 8 cell rep = phi[2,1,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 8*X TII subcells: tii[2,1] := {0} tii[2,2] := {1} tii[2,3] := {2} tii[2,4] := {3} tii[2,5] := {4} tii[2,6] := {6} tii[2,7] := {7} tii[2,8] := {5} cell#13 , |C| = 1 special orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1] special rep = [1, 1, 1, 1, 1, 1, 1, 1, 1] , dim = 1 cell rep = phi[1,1,1,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = X TII subcells: tii[1,1] := {0}