TII subcells for the U(5,2) x GL(7,R) block of GL7 # cell#0 , |C| = 15 special orbit = [5, 1, 1] special rep = [5, 1, 1] , dim = 15 cell rep = phi[5,1,1] TII depth = 1 TII multiplicity polynomial = 15*X TII subcells: tii[12,1] := {0} tii[12,2] := {9} tii[12,3] := {1} tii[12,4] := {6} tii[12,5] := {3} tii[12,6] := {14} tii[12,7] := {10} tii[12,8] := {12} tii[12,9] := {11} tii[12,10] := {2} tii[12,11] := {7} tii[12,12] := {4} tii[12,13] := {13} tii[12,14] := {8} tii[12,15] := {5} cell#1 , |C| = 20 special orbit = [4, 1, 1, 1] special rep = [4, 1, 1, 1] , dim = 20 cell rep = phi[4,1,1,1] TII depth = 1 TII multiplicity polynomial = 20*X TII subcells: tii[9,1] := {2} tii[9,2] := {7} tii[9,3] := {0} tii[9,4] := {4} tii[9,5] := {14} tii[9,6] := {8} tii[9,7] := {10} tii[9,8] := {1} tii[9,9] := {5} tii[9,10] := {12} tii[9,11] := {19} tii[9,12] := {15} tii[9,13] := {17} tii[9,14] := {9} tii[9,15] := {11} tii[9,16] := {16} tii[9,17] := {3} tii[9,18] := {6} tii[9,19] := {13} tii[9,20] := {18} cell#2 , |C| = 21 special orbit = [3, 3, 1] special rep = [3, 3, 1] , dim = 21 cell rep = phi[3,3,1] TII depth = 2 TII multiplicity polynomial = 21*X TII subcells: tii[8,1] := {11} tii[8,2] := {18} tii[8,3] := {19} tii[8,4] := {20} tii[8,5] := {17} tii[8,6] := {12} tii[8,7] := {2} tii[8,8] := {6} tii[8,9] := {15} tii[8,10] := {4} tii[8,11] := {8} tii[8,12] := {3} tii[8,13] := {14} tii[8,14] := {10} tii[8,15] := {13} tii[8,16] := {16} tii[8,17] := {7} tii[8,18] := {5} tii[8,19] := {0} tii[8,20] := {9} tii[8,21] := {1} cell#3 , |C| = 35 special orbit = [3, 2, 1, 1] special rep = [3, 2, 1, 1] , dim = 35 cell rep = phi[3,2,1,1] TII depth = 2 TII multiplicity polynomial = 35*X TII subcells: tii[6,1] := {2} tii[6,2] := {7} tii[6,3] := {6} tii[6,4] := {15} tii[6,5] := {12} tii[6,6] := {20} tii[6,7] := {23} tii[6,8] := {14} tii[6,9] := {13} tii[6,10] := {27} tii[6,11] := {22} tii[6,12] := {29} tii[6,13] := {28} tii[6,14] := {32} tii[6,15] := {26} tii[6,16] := {33} tii[6,17] := {30} tii[6,18] := {34} tii[6,19] := {31} tii[6,20] := {25} tii[6,21] := {0} tii[6,22] := {1} tii[6,23] := {5} tii[6,24] := {3} tii[6,25] := {10} tii[6,26] := {4} tii[6,27] := {16} tii[6,28] := {9} tii[6,29] := {24} tii[6,30] := {21} tii[6,31] := {8} tii[6,32] := {11} tii[6,33] := {18} tii[6,34] := {19} tii[6,35] := {17} cell#4 , |C| = 20 special orbit = [4, 1, 1, 1] special rep = [4, 1, 1, 1] , dim = 20 cell rep = phi[4,1,1,1] TII depth = 1 TII multiplicity polynomial = 20*X TII subcells: tii[9,1] := {19} tii[9,2] := {14} tii[9,3] := {17} tii[9,4] := {15} tii[9,5] := {7} tii[9,6] := {10} tii[9,7] := {8} tii[9,8] := {16} tii[9,9] := {11} tii[9,10] := {9} tii[9,11] := {0} tii[9,12] := {4} tii[9,13] := {1} tii[9,14] := {12} tii[9,15] := {5} tii[9,16] := {2} tii[9,17] := {18} tii[9,18] := {13} tii[9,19] := {6} tii[9,20] := {3} cell#5 , |C| = 14 special orbit = [2, 2, 1, 1, 1] special rep = [2, 2, 1, 1, 1] , dim = 14 cell rep = phi[2,2,1,1,1] TII depth = 1 TII multiplicity polynomial = 14*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] := {12} tii[3,10] := {13} tii[3,11] := {0} tii[3,12] := {2} tii[3,13] := {6} tii[3,14] := {11} cell#6 , |C| = 15 special orbit = [3, 1, 1, 1, 1] special rep = [3, 1, 1, 1, 1] , dim = 15 cell rep = phi[3,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 15*X TII subcells: tii[5,1] := {14} tii[5,2] := {9} tii[5,3] := {11} tii[5,4] := {5} tii[5,5] := {7} tii[5,6] := {12} tii[5,7] := {2} tii[5,8] := {3} tii[5,9] := {6} tii[5,10] := {10} tii[5,11] := {0} tii[5,12] := {1} tii[5,13] := {4} tii[5,14] := {8} tii[5,15] := {13} cell#7 , |C| = 35 special orbit = [3, 2, 1, 1] special rep = [3, 2, 1, 1] , dim = 35 cell rep = phi[3,2,1,1] TII depth = 2 TII multiplicity polynomial = 35*X TII subcells: tii[6,1] := {27} tii[6,2] := {29} tii[6,3] := {32} tii[6,4] := {33} tii[6,5] := {26} tii[6,6] := {17} tii[6,7] := {30} tii[6,8] := {22} tii[6,9] := {34} tii[6,10] := {23} tii[6,11] := {31} tii[6,12] := {25} tii[6,13] := {24} tii[6,14] := {20} tii[6,15] := {11} tii[6,16] := {15} tii[6,17] := {7} tii[6,18] := {10} tii[6,19] := {4} tii[6,20] := {1} tii[6,21] := {18} tii[6,22] := {12} tii[6,23] := {19} tii[6,24] := {21} tii[6,25] := {9} tii[6,26] := {6} tii[6,27] := {16} tii[6,28] := {28} tii[6,29] := {8} tii[6,30] := {3} tii[6,31] := {13} tii[6,32] := {2} tii[6,33] := {14} tii[6,34] := {5} tii[6,35] := {0} cell#8 , |C| = 14 special orbit = [2, 2, 1, 1, 1] special rep = [2, 2, 1, 1, 1] , dim = 14 cell rep = phi[2,2,1,1,1] TII depth = 1 TII multiplicity polynomial = 14*X TII subcells: tii[3,1] := {13} tii[3,2] := {11} tii[3,3] := {9} tii[3,4] := {10} tii[3,5] := {8} tii[3,6] := {5} tii[3,7] := {7} tii[3,8] := {4} tii[3,9] := {2} tii[3,10] := {1} tii[3,11] := {12} tii[3,12] := {6} tii[3,13] := {3} tii[3,14] := {0} cell#9 , |C| = 15 special orbit = [3, 1, 1, 1, 1] special rep = [3, 1, 1, 1, 1] , dim = 15 cell rep = phi[3,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 15*X TII subcells: tii[5,1] := {1} tii[5,2] := {3} tii[5,3] := {7} tii[5,4] := {6} tii[5,5] := {11} tii[5,6] := {8} tii[5,7] := {13} tii[5,8] := {14} tii[5,9] := {12} tii[5,10] := {9} tii[5,11] := {5} tii[5,12] := {10} tii[5,13] := {4} tii[5,14] := {2} tii[5,15] := {0} cell#10 , |C| = 14 special orbit = [2, 2, 1, 1, 1] special rep = [2, 2, 1, 1, 1] , dim = 14 cell rep = phi[2,2,1,1,1] TII depth = 1 TII multiplicity polynomial = 14*X TII subcells: tii[3,1] := {7} tii[3,2] := {10} tii[3,3] := {6} tii[3,4] := {12} tii[3,5] := {9} tii[3,6] := {5} tii[3,7] := {13} tii[3,8] := {11} tii[3,9] := {8} tii[3,10] := {4} tii[3,11] := {1} tii[3,12] := {2} tii[3,13] := {3} tii[3,14] := {0} cell#11 , |C| = 6 special orbit = [2, 1, 1, 1, 1, 1] special rep = [2, 1, 1, 1, 1, 1] , dim = 6 cell rep = phi[2,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 6*X TII subcells: tii[2,1] := {3} tii[2,2] := {5} tii[2,3] := {4} tii[2,4] := {2} tii[2,5] := {1} tii[2,6] := {0} cell#12 , |C| = 6 special orbit = [2, 1, 1, 1, 1, 1] special rep = [2, 1, 1, 1, 1, 1] , dim = 6 cell rep = phi[2,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = 6*X TII subcells: tii[2,1] := {0} tii[2,2] := {1} tii[2,3] := {2} tii[2,4] := {4} tii[2,5] := {5} tii[2,6] := {3} cell#13 , |C| = 1 special orbit = [1, 1, 1, 1, 1, 1, 1] special rep = [1, 1, 1, 1, 1, 1, 1] , dim = 1 cell rep = phi[1,1,1,1,1,1,1] TII depth = 1 TII multiplicity polynomial = X TII subcells: tii[1,1] := {0}