TII subcells for the Sp(14,R) x SO(12,3) block of Sp14 # cell#0 , |C| = 1 special orbit = [14] special rep = [[7], []] , dim = 1 cell rep = phi[[7],[]] TII depth = 1 TII multiplicity polynomial = X TII subcells: tii[40,1] := {0} cell#1 , |C| = 1 special orbit = [14] special rep = [[7], []] , dim = 1 cell rep = phi[[7],[]] TII depth = 1 TII multiplicity polynomial = X TII subcells: tii[40,1] := {0} cell#2 , |C| = 13 special orbit = [12, 2] special rep = [[6], [1]] , dim = 7 cell rep = phi[[6, 1],[]]+phi[[6],[1]] TII depth = 1 TII multiplicity polynomial = X+6*X^2 TII subcells: tii[39,1] := {1, 9} tii[39,2] := {0, 6} tii[39,3] := {2, 3} tii[39,4] := {4, 5} tii[39,5] := {7, 8} tii[39,6] := {10, 11} tii[39,7] := {12} cell#3 , |C| = 13 special orbit = [12, 2] special rep = [[6], [1]] , dim = 7 cell rep = phi[[6, 1],[]]+phi[[6],[1]] TII depth = 1 TII multiplicity polynomial = X+6*X^2 TII subcells: tii[39,1] := {0, 12} tii[39,2] := {1, 11} tii[39,3] := {2, 10} tii[39,4] := {3, 9} tii[39,5] := {4, 8} tii[39,6] := {5, 7} tii[39,7] := {6} cell#4 , |C| = 13 special orbit = [12, 2] special rep = [[6], [1]] , dim = 7 cell rep = phi[[6, 1],[]]+phi[[6],[1]] TII depth = 1 TII multiplicity polynomial = X+6*X^2 TII subcells: tii[39,1] := {1, 9} tii[39,2] := {0, 6} tii[39,3] := {2, 3} tii[39,4] := {4, 5} tii[39,5] := {7, 8} tii[39,6] := {10, 11} tii[39,7] := {12} cell#5 , |C| = 13 special orbit = [12, 2] special rep = [[6], [1]] , dim = 7 cell rep = phi[[6, 1],[]]+phi[[6],[1]] TII depth = 1 TII multiplicity polynomial = X+6*X^2 TII subcells: tii[39,1] := {0, 12} tii[39,2] := {1, 11} tii[39,3] := {2, 10} tii[39,4] := {3, 9} tii[39,5] := {4, 8} tii[39,6] := {5, 7} tii[39,7] := {6} cell#6 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {5} tii[37,2] := {15} tii[37,3] := {25} tii[37,4] := {31} tii[37,5] := {34} tii[37,6] := {0} tii[37,7] := {1} tii[37,8] := {2} tii[37,9] := {3} tii[37,10] := {4} tii[37,11] := {7} tii[37,12] := {8} tii[37,13] := {11} tii[37,14] := {12} tii[37,15] := {17} tii[37,16] := {6} tii[37,17] := {10} tii[37,18] := {9} tii[37,19] := {14} tii[37,20] := {13} tii[37,21] := {19} tii[37,22] := {18} tii[37,23] := {22} tii[37,24] := {16} tii[37,25] := {21} tii[37,26] := {20} tii[37,27] := {24} tii[37,28] := {23} tii[37,29] := {27} tii[37,30] := {26} tii[37,31] := {29} tii[37,32] := {28} tii[37,33] := {30} tii[37,34] := {32} tii[37,35] := {33} cell#7 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {5} tii[37,2] := {15} tii[37,3] := {25} tii[37,4] := {31} tii[37,5] := {34} tii[37,6] := {0} tii[37,7] := {1} tii[37,8] := {2} tii[37,9] := {3} tii[37,10] := {4} tii[37,11] := {7} tii[37,12] := {8} tii[37,13] := {11} tii[37,14] := {12} tii[37,15] := {17} tii[37,16] := {6} tii[37,17] := {10} tii[37,18] := {9} tii[37,19] := {14} tii[37,20] := {13} tii[37,21] := {19} tii[37,22] := {18} tii[37,23] := {22} tii[37,24] := {16} tii[37,25] := {21} tii[37,26] := {20} tii[37,27] := {24} tii[37,28] := {23} tii[37,29] := {27} tii[37,30] := {26} tii[37,31] := {29} tii[37,32] := {28} tii[37,33] := {30} tii[37,34] := {32} tii[37,35] := {33} cell#8 , |C| = 35 special orbit = [10, 4] special rep = [[5], [2]] , dim = 21 cell rep = phi[[5, 2],[]]+phi[[5],[2]] TII depth = 1 TII multiplicity polynomial = 7*X+14*X^2 TII subcells: tii[38,1] := {4, 5} tii[38,2] := {14, 15} tii[38,3] := {24, 25} tii[38,4] := {30, 31} tii[38,5] := {33} tii[38,6] := {34} tii[38,7] := {0, 1} tii[38,8] := {2, 3} tii[38,9] := {6, 7} tii[38,10] := {10, 11} tii[38,11] := {16} tii[38,12] := {8, 9} tii[38,13] := {12, 13} tii[38,14] := {17, 18} tii[38,15] := {21} tii[38,16] := {19, 20} tii[38,17] := {22, 23} tii[38,18] := {26} tii[38,19] := {27, 28} tii[38,20] := {29} tii[38,21] := {32} cell#9 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {34} tii[37,2] := {33} tii[37,3] := {32} tii[37,4] := {31} tii[37,5] := {30} tii[37,6] := {0} tii[37,7] := {29} tii[37,8] := {1} tii[37,9] := {24} tii[37,10] := {2} tii[37,11] := {19} tii[37,12] := {4} tii[37,13] := {15} tii[37,14] := {6} tii[37,15] := {11} tii[37,16] := {3} tii[37,17] := {5} tii[37,18] := {28} tii[37,19] := {7} tii[37,20] := {23} tii[37,21] := {9} tii[37,22] := {18} tii[37,23] := {14} tii[37,24] := {8} tii[37,25] := {10} tii[37,26] := {27} tii[37,27] := {12} tii[37,28] := {22} tii[37,29] := {17} tii[37,30] := {13} tii[37,31] := {16} tii[37,32] := {26} tii[37,33] := {21} tii[37,34] := {20} tii[37,35] := {25} cell#10 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {34} tii[37,2] := {33} tii[37,3] := {32} tii[37,4] := {31} tii[37,5] := {30} tii[37,6] := {0} tii[37,7] := {29} tii[37,8] := {1} tii[37,9] := {24} tii[37,10] := {2} tii[37,11] := {19} tii[37,12] := {4} tii[37,13] := {15} tii[37,14] := {6} tii[37,15] := {11} tii[37,16] := {3} tii[37,17] := {5} tii[37,18] := {28} tii[37,19] := {7} tii[37,20] := {23} tii[37,21] := {9} tii[37,22] := {18} tii[37,23] := {14} tii[37,24] := {8} tii[37,25] := {10} tii[37,26] := {27} tii[37,27] := {12} tii[37,28] := {22} tii[37,29] := {17} tii[37,30] := {13} tii[37,31] := {16} tii[37,32] := {26} tii[37,33] := {21} tii[37,34] := {20} tii[37,35] := {25} cell#11 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {25} tii[37,2] := {8} tii[37,3] := {24} tii[37,4] := {32} tii[37,5] := {34} tii[37,6] := {4} tii[37,7] := {17} tii[37,8] := {3} tii[37,9] := {10} tii[37,10] := {9} tii[37,11] := {16} tii[37,12] := {15} tii[37,13] := {22} tii[37,14] := {21} tii[37,15] := {27} tii[37,16] := {0} tii[37,17] := {1} tii[37,18] := {2} tii[37,19] := {5} tii[37,20] := {6} tii[37,21] := {11} tii[37,22] := {12} tii[37,23] := {18} tii[37,24] := {7} tii[37,25] := {13} tii[37,26] := {14} tii[37,27] := {19} tii[37,28] := {20} tii[37,29] := {26} tii[37,30] := {23} tii[37,31] := {28} tii[37,32] := {29} tii[37,33] := {30} tii[37,34] := {31} tii[37,35] := {33} cell#12 , |C| = 35 special orbit = [10, 2, 2] special rep = [[5, 1], [1]] , dim = 35 cell rep = phi[[5, 1],[1]] TII depth = 5 TII multiplicity polynomial = 35*X TII subcells: tii[37,1] := {25} tii[37,2] := {7} tii[37,3] := {23} tii[37,4] := {31} tii[37,5] := {34} tii[37,6] := {4} tii[37,7] := {17} tii[37,8] := {3} tii[37,9] := {9} tii[37,10] := {10} tii[37,11] := {15} tii[37,12] := {16} tii[37,13] := {21} tii[37,14] := {22} tii[37,15] := {27} tii[37,16] := {0} tii[37,17] := {2} tii[37,18] := {1} tii[37,19] := {6} tii[37,20] := {5} tii[37,21] := {12} tii[37,22] := {11} tii[37,23] := {18} tii[37,24] := {8} tii[37,25] := {14} tii[37,26] := {13} tii[37,27] := {20} tii[37,28] := {19} tii[37,29] := {26} tii[37,30] := {24} tii[37,31] := {29} tii[37,32] := {28} tii[37,33] := {30} tii[37,34] := {32} tii[37,35] := {33} cell#13 , |C| = 36 special orbit = [10, 2, 1, 1] special rep = [[5], [1, 1]] , dim = 21 cell rep = phi[[5, 1, 1],[]]+phi[[5],[1, 1]] TII depth = 1 TII multiplicity polynomial = 6*X+15*X^2 TII subcells: tii[36,1] := {1, 35} tii[36,2] := {3, 34} tii[36,3] := {6, 33} tii[36,4] := {9, 25} tii[36,5] := {11, 21} tii[36,6] := {16} tii[36,7] := {0, 32} tii[36,8] := {2, 27} tii[36,9] := {4, 22} tii[36,10] := {7, 17} tii[36,11] := {13} tii[36,12] := {5, 31} tii[36,13] := {8, 26} tii[36,14] := {10, 20} tii[36,15] := {15} tii[36,16] := {12, 30} tii[36,17] := {14, 24} tii[36,18] := {19} tii[36,19] := {18, 29} tii[36,20] := {23} tii[36,21] := {28} cell#14 , |C| = 36 special orbit = [10, 2, 1, 1] special rep = [[5], [1, 1]] , dim = 21 cell rep = phi[[5, 1, 1],[]]+phi[[5],[1, 1]] TII depth = 1 TII multiplicity polynomial = 6*X+15*X^2 TII subcells: tii[36,1] := {1, 35} tii[36,2] := {3, 34} tii[36,3] := {6, 33} tii[36,4] := {9, 25} tii[36,5] := {11, 21} tii[36,6] := {16} tii[36,7] := {0, 32} tii[36,8] := {2, 27} tii[36,9] := {4, 22} tii[36,10] := {7, 17} tii[36,11] := {13} tii[36,12] := {5, 31} tii[36,13] := {8, 26} tii[36,14] := {10, 20} tii[36,15] := {15} tii[36,16] := {12, 30} tii[36,17] := {14, 24} tii[36,18] := {19} tii[36,19] := {18, 29} tii[36,20] := {23} tii[36,21] := {28} cell#15 , |C| = 147 special orbit = [8, 4, 2] special rep = [[4, 1], [2]] , dim = 84 cell rep = phi[[4, 2],[1]]+phi[[4, 1],[2]] TII depth = 4 TII multiplicity polynomial = 21*X+63*X^2 TII subcells: tii[34,1] := {72, 75} tii[34,2] := {121, 124} tii[34,3] := {141, 142} tii[34,4] := {146} tii[34,5] := {6, 7} tii[34,6] := {35, 36} tii[34,7] := {24, 27} tii[34,8] := {78, 79} tii[34,9] := {64, 67} tii[34,10] := {102, 103} tii[34,11] := {112} tii[34,12] := {127} tii[34,13] := {18, 19} tii[34,14] := {49, 52} tii[34,15] := {12, 13} tii[34,16] := {58, 59} tii[34,17] := {98, 99} tii[34,18] := {28, 31} tii[34,19] := {29, 30} tii[34,20] := {88, 91} tii[34,21] := {117, 118} tii[34,22] := {45, 48} tii[34,23] := {46, 47} tii[34,24] := {125} tii[34,25] := {62, 63} tii[34,26] := {136} tii[34,27] := {82, 83} tii[34,28] := {108, 111} tii[34,29] := {73, 74} tii[34,30] := {115, 116} tii[34,31] := {93, 94} tii[34,32] := {92, 95} tii[34,33] := {130, 131} tii[34,34] := {134} tii[34,35] := {106, 107} tii[34,36] := {140} tii[34,37] := {128, 129} tii[34,38] := {137, 138} tii[34,39] := {122, 123} tii[34,40] := {139} tii[34,41] := {132, 133} tii[34,42] := {144} tii[34,43] := {143} tii[34,44] := {145} tii[34,45] := {0, 1} tii[34,46] := {4, 5} tii[34,47] := {14, 15} tii[34,48] := {32} tii[34,49] := {2, 3} tii[34,50] := {9, 10} tii[34,51] := {8, 11} tii[34,52] := {16, 17} tii[34,53] := {21, 22} tii[34,54] := {20, 23} tii[34,55] := {33, 34} tii[34,56] := {39, 40} tii[34,57] := {53} tii[34,58] := {25, 26} tii[34,59] := {42, 43} tii[34,60] := {41, 44} tii[34,61] := {54, 55} tii[34,62] := {60, 61} tii[34,63] := {76} tii[34,64] := {65, 66} tii[34,65] := {96} tii[34,66] := {84, 85} tii[34,67] := {37, 38} tii[34,68] := {56, 57} tii[34,69] := {77} tii[34,70] := {50, 51} tii[34,71] := {80, 81} tii[34,72] := {69, 70} tii[34,73] := {68, 71} tii[34,74] := {86, 87} tii[34,75] := {97} tii[34,76] := {89, 90} tii[34,77] := {113} tii[34,78] := {104, 105} tii[34,79] := {100, 101} tii[34,80] := {114} tii[34,81] := {109, 110} tii[34,82] := {126} tii[34,83] := {119, 120} tii[34,84] := {135} cell#16 , |C| = 154 special orbit = [8, 2, 2, 2] special rep = [[4, 1], [1, 1]] , dim = 84 cell rep = phi[[4, 1, 1],[1]]+phi[[4, 1],[1, 1]] TII depth = 4 TII multiplicity polynomial = 14*X+70*X^2 TII subcells: tii[32,1] := {6, 129} tii[32,2] := {23, 126} tii[32,3] := {50, 122} tii[32,4] := {77, 119} tii[32,5] := {14, 134} tii[32,6] := {38, 141} tii[32,7] := {18, 116} tii[32,8] := {69, 138} tii[32,9] := {31, 109} tii[32,10] := {99, 137} tii[32,11] := {42, 86} tii[32,12] := {65} tii[32,13] := {54, 145} tii[32,14] := {90, 148} tii[32,15] := {60, 133} tii[32,16] := {120, 147} tii[32,17] := {76, 128} tii[32,18] := {103} tii[32,19] := {111, 151} tii[32,20] := {136, 152} tii[32,21] := {117, 144} tii[32,22] := {140} tii[32,23] := {146, 153} tii[32,24] := {150} tii[32,25] := {0, 3} tii[32,26] := {1, 110} tii[32,27] := {2, 9} tii[32,28] := {4, 88} tii[32,29] := {5, 17} tii[32,30] := {10, 68} tii[32,31] := {11, 28} tii[32,32] := {20, 47} tii[32,33] := {7, 19} tii[32,34] := {8, 95} tii[32,35] := {16, 89} tii[32,36] := {13, 30} tii[32,37] := {12, 108} tii[32,38] := {27, 67} tii[32,39] := {22, 41} tii[32,40] := {21, 85} tii[32,41] := {46} tii[32,42] := {33, 64} tii[32,43] := {24, 43} tii[32,44] := {29, 94} tii[32,45] := {35, 57} tii[32,46] := {40, 87} tii[32,47] := {34, 105} tii[32,48] := {63} tii[32,49] := {48, 80} tii[32,50] := {51, 73} tii[32,51] := {56, 93} tii[32,52] := {83} tii[32,53] := {62, 101} tii[32,54] := {92} tii[32,55] := {15, 32} tii[32,56] := {25, 130} tii[32,57] := {26, 45} tii[32,58] := {36, 106} tii[32,59] := {37, 59} tii[32,60] := {49, 82} tii[32,61] := {39, 61} tii[32,62] := {44, 115} tii[32,63] := {53, 75} tii[32,64] := {52, 127} tii[32,65] := {58, 107} tii[32,66] := {66, 102} tii[32,67] := {81} tii[32,68] := {70, 96} tii[32,69] := {74, 114} tii[32,70] := {104} tii[32,71] := {79, 123} tii[32,72] := {113} tii[32,73] := {55, 78} tii[32,74] := {71, 142} tii[32,75] := {72, 98} tii[32,76] := {84, 124} tii[32,77] := {91, 118} tii[32,78] := {97, 132} tii[32,79] := {100, 139} tii[32,80] := {125} tii[32,81] := {131} tii[32,82] := {112, 135} tii[32,83] := {121, 149} tii[32,84] := {143} cell#17 , |C| = 154 special orbit = [8, 2, 2, 2] special rep = [[4, 1], [1, 1]] , dim = 84 cell rep = phi[[4, 1, 1],[1]]+phi[[4, 1],[1, 1]] TII depth = 4 TII multiplicity polynomial = 14*X+70*X^2 TII subcells: tii[32,1] := {6, 129} tii[32,2] := {23, 126} tii[32,3] := {50, 122} tii[32,4] := {77, 119} tii[32,5] := {14, 134} tii[32,6] := {38, 141} tii[32,7] := {18, 116} tii[32,8] := {69, 138} tii[32,9] := {31, 109} tii[32,10] := {99, 137} tii[32,11] := {42, 86} tii[32,12] := {65} tii[32,13] := {54, 145} tii[32,14] := {90, 148} tii[32,15] := {60, 133} tii[32,16] := {120, 147} tii[32,17] := {76, 128} tii[32,18] := {103} tii[32,19] := {111, 151} tii[32,20] := {136, 152} tii[32,21] := {117, 144} tii[32,22] := {140} tii[32,23] := {146, 153} tii[32,24] := {150} tii[32,25] := {0, 3} tii[32,26] := {1, 110} tii[32,27] := {2, 9} tii[32,28] := {4, 88} tii[32,29] := {5, 17} tii[32,30] := {10, 68} tii[32,31] := {11, 28} tii[32,32] := {20, 47} tii[32,33] := {7, 19} tii[32,34] := {8, 95} tii[32,35] := {16, 89} tii[32,36] := {13, 30} tii[32,37] := {12, 108} tii[32,38] := {27, 67} tii[32,39] := {22, 41} tii[32,40] := {21, 85} tii[32,41] := {46} tii[32,42] := {33, 64} tii[32,43] := {24, 43} tii[32,44] := {29, 94} tii[32,45] := {35, 57} tii[32,46] := {40, 87} tii[32,47] := {34, 105} tii[32,48] := {63} tii[32,49] := {48, 80} tii[32,50] := {51, 73} tii[32,51] := {56, 93} tii[32,52] := {83} tii[32,53] := {62, 101} tii[32,54] := {92} tii[32,55] := {15, 32} tii[32,56] := {25, 130} tii[32,57] := {26, 45} tii[32,58] := {36, 106} tii[32,59] := {37, 59} tii[32,60] := {49, 82} tii[32,61] := {39, 61} tii[32,62] := {44, 115} tii[32,63] := {53, 75} tii[32,64] := {52, 127} tii[32,65] := {58, 107} tii[32,66] := {66, 102} tii[32,67] := {81} tii[32,68] := {70, 96} tii[32,69] := {74, 114} tii[32,70] := {104} tii[32,71] := {79, 123} tii[32,72] := {113} tii[32,73] := {55, 78} tii[32,74] := {71, 142} tii[32,75] := {72, 98} tii[32,76] := {84, 124} tii[32,77] := {91, 118} tii[32,78] := {97, 132} tii[32,79] := {100, 139} tii[32,80] := {125} tii[32,81] := {131} tii[32,82] := {112, 135} tii[32,83] := {121, 149} tii[32,84] := {143} cell#18 , |C| = 36 special orbit = [10, 2, 1, 1] special rep = [[5], [1, 1]] , dim = 21 cell rep = phi[[5, 1, 1],[]]+phi[[5],[1, 1]] TII depth = 1 TII multiplicity polynomial = 6*X+15*X^2 TII subcells: tii[36,1] := {1, 2} tii[36,2] := {11, 12} tii[36,3] := {20, 21} tii[36,4] := {27, 28} tii[36,5] := {32, 33} tii[36,6] := {35} tii[36,7] := {9, 10} tii[36,8] := {18, 19} tii[36,9] := {25, 26} tii[36,10] := {30, 31} tii[36,11] := {34} tii[36,12] := {7, 8} tii[36,13] := {16, 17} tii[36,14] := {23, 24} tii[36,15] := {29} tii[36,16] := {5, 6} tii[36,17] := {14, 15} tii[36,18] := {22} tii[36,19] := {3, 4} tii[36,20] := {13} tii[36,21] := {0} cell#19 , |C| = 55 special orbit = [8, 2, 1, 1, 1, 1] special rep = [[4], [1, 1, 1]] , dim = 35 cell rep = phi[[4, 1, 1, 1],[]]+phi[[4],[1, 1, 1]] TII depth = 1 TII multiplicity polynomial = 15*X+20*X^2 TII subcells: tii[31,1] := {1, 2} tii[31,2] := {10, 12} tii[31,3] := {25, 28} tii[31,4] := {41, 45} tii[31,5] := {54} tii[31,6] := {7, 8} tii[31,7] := {21, 22} tii[31,8] := {36, 37} tii[31,9] := {49} tii[31,10] := {5, 6} tii[31,11] := {17, 18} tii[31,12] := {31} tii[31,13] := {3, 4} tii[31,14] := {14} tii[31,15] := {0} tii[31,16] := {9, 11} tii[31,17] := {24, 27} tii[31,18] := {40, 44} tii[31,19] := {53} tii[31,20] := {19, 20} tii[31,21] := {34, 35} tii[31,22] := {48} tii[31,23] := {15, 16} tii[31,24] := {30} tii[31,25] := {13} tii[31,26] := {23, 26} tii[31,27] := {39, 43} tii[31,28] := {52} tii[31,29] := {32, 33} tii[31,30] := {47} tii[31,31] := {29} tii[31,32] := {38, 42} tii[31,33] := {51} tii[31,34] := {46} tii[31,35] := {50}