#From John Stembridge # representatives from the 107 cells that are maximal with respect to # the property that they are psd in all irreps of W(E7). # Format: fund.wt.coords co-dim J <1 =1 >1 # overall f-vector: [8, 32, 70, 119, 209, 246, 171, 63] [0, 0, 0, 0, 0, 0, 0] 0 {} {63} {} {} [0, 0, 1/4, 3/32, 0, 0, 0] 0 {} {61} {} {62} [0, 11/32, 0, 0, 1/8, 0, 0] 0 {} {58, 59} {} {60} [0, 1/4, 3/16, 0, 0, 0, 1/4] 0 {} {53, 59} {} {56} [0, 1/8, 3/32, 1/8, 0, 1/8, 1/8] 0 {} {53, 54, 55} {} {56, 57} [1/8, 1/8, 7/48, 0, 0, 13/48, 1/8] 0 {} {49, 53, 54} {} {52, 56} [1/8, 0, 1/8, 1/16, 1/8, 1/8, 3/16] 0 {} {47, 48, 49, 53} {} {51, 52} [1/16, 15/32, 1/16, 1/16, 1/16, 1/16, 1/16] 0 {} {46, 47, 48, 49} {} {50, 51, 52} [1/8, 7/16, 1/8, 1/16, 1/16, 1/16, 1/16] 4 {} {38, 39, 45} {37, 43, 44 , 49} {42, 48} [3/16, 3/8, 1/8, 1/16, 1/16, 1/16, 1/8] 4 {} {34, 38, 45} {37, 39, 43, 49} {42, 44} [19/64, 1/16, 15/64, 0, 11/64, 1/16, 15/64] 4 {} {38, 45} {34, 37, 43, 49} {39, 42} [3/16, 1/2, 1/16, 1/16, 1/16, 1/16, 1/16] 4 {} {32, 33, 34, 45} {37, 38 , 39, 49} {42, 43, 44} [3/8, 1/16, 3/16, 1/16, 1/16, 3/16, 1/8] 4 {} {32, 33, 45} {34, 37, 38 , 49} {39, 42, 43} [19/48, 1/16, 5/24, 1/16, 0, 13/48, 1/16] 4 {} {27, 32, 45} {33, 34, 37 , 49} {38, 39} [3/8, 1/8, 1/4, 1/8, 0, 1/8, 1/8] 4 {} {26, 27, 45} {32, 33, 34, 49} {37, 38, 39} [1/2, 1/8, 3/8, 0, 1/8, 1/8, 0] 3 {} {14, 45} {20, 21, 49} {26, 27} [1/8, 0, 1/8, 1/8, 1/8, 1/4, 1/8] 4 {} {37, 38, 39, 40, 41} {42, 43, 44 , 45} {46, 47, 48, 49} [1/8, 1/16, 1/16, 1/16, 1/16, 1/2, 1/8] 4 {} {34, 37, 38, 40, 41} {39, 42, 43, 45} {44, 46, 49} [1/4, 1/8, 1/8, 0, 1/8, 1/4, 1/4] 4 {} {37, 38, 40, 41} {34, 42, 43, 45 } {39, 46, 49} [1/4, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8] 4 {} {32, 33, 34, 40, 41} {37, 38, 39, 45} {42, 43, 44, 49} [3/16, 1/16, 9/32, 1/16, 1/16, 9/32, 1/8] 4 {} {32, 33, 40, 41} {34, 37 , 38, 45} {39, 42, 43, 49} [3/16, 1/16, 9/32, 1/16, 1/16, 11/32, 1/16] 4 {} {27, 32, 40, 41} {33, 34, 37, 45} {38, 39, 49} [3/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8] 4 {} {26, 27, 40, 41} {32, 33, 34, 45} {37, 38, 39, 49} [1/2, 1/4, 1/4, 0, 1/8, 1/8, 1/8] 3 {} {21, 40, 41} {20, 27, 45} {26 , 34, 49} [1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/4] 4 {} {34, 36, 37, 38, 40} {39, 41, 42, 43} {44, 45, 46} [1/8, 1/16, 1/16, 1/16, 1/16, 1/2, 3/16] 4 {} {36, 37, 38, 40} {34, 41 , 42, 43} {39, 45, 46} [1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 3/8] 4 {} {30, 31, 37, 38, 40} {34, 36, 42, 43} {39, 41, 46} [1/8, 1/4, 1/8, 0, 1/8, 1/4, 3/8] 4 {} {31, 37, 38, 40} {30, 34, 42, 43 } {36, 46} [1/8, 1/8, 1/8, 0, 1/8, 3/8, 3/8] 4 {} {25, 37, 38, 40} {30, 31, 42, 43 } {34, 36, 46} [1/16, 1/2, 1/8, 1/16, 1/16, 1/16, 1/8] 4 {} {34, 36, 38, 40} {37, 39, 41, 43} {42, 44, 45} [1/8, 1/16, 5/16, 1/16, 1/16, 1/4, 3/16] 4 {} {36, 38, 40} {34, 37, 41 , 43} {39, 42, 45} [1/16, 1/16, 11/32, 1/16, 1/16, 9/32, 3/16] 4 {} {30, 31, 38, 40} {34, 36, 37, 43} {39, 41, 42} [1/16, 3/16, 1/8, 7/32, 1/16, 1/16, 15/32] 4 {} {31, 38, 40} {30, 34, 37, 43} {36, 42} [1/8, 1/4, 1/4, 0, 1/8, 1/8, 1/2] 4 {} {25, 38, 40} {30, 31, 37, 43} {34, 36, 42} [1/16, 1/16, 1/16, 1/16, 1/8, 1/2, 1/8] 4 {} {34, 36, 37, 38} {39, 40, 41, 42} {43, 44, 45} [1/8, 1/16, 1/16, 1/16, 3/16, 3/8, 3/16] 4 {} {36, 37, 38} {34, 40, 41 , 42} {39, 43, 45} [1/16, 1/16, 1/16, 1/16, 1/8, 1/2, 3/16] 4 {} {30, 31, 37, 38} {34, 36 , 40, 42} {39, 41, 43} [1/8, 1/4, 1/8, 0, 1/4, 1/8, 3/8] 4 {} {31, 37, 38} {30, 34, 40, 42} {36, 43} [1/8, 1/2, 1/16, 1/16, 1/8, 1/16, 1/16] 4 {} {32, 33, 34, 41} {37, 38, 39, 40} {42, 43, 44, 45} [1/16, 1/16, 5/16, 1/16, 1/8, 1/4, 1/8] 4 {} {34, 36, 38} {37, 39, 40, 41} {42, 43, 44, 45} [1/8, 1/8, 1/8, 1/8, 1/8, 1/4, 1/8] 4 {} {33, 34, 35, 36, 37} {38, 39, 40, 41} {42, 43, 44, 45} [3/16, 1/16, 7/32, 1/16, 3/16, 7/32, 1/8] 4 {} {32, 33, 41} {34, 37, 38 , 40} {39, 42, 43, 45} [1/8, 1/16, 1/4, 1/16, 3/16, 3/16, 3/16] 4 {} {36, 38} {34, 37, 40, 41} {39, 42, 43, 45} [1/8, 1/16, 1/4, 1/16, 1/8, 5/16, 1/8] 4 {} {33, 35, 36, 37} {34, 38, 40, 41} {39, 42, 43, 45} [3/16, 1/16, 1/4, 1/16, 1/8, 5/16, 1/16] 4 {} {27, 32, 41} {33, 34, 37 , 40} {38, 39, 45} [3/16, 1/8, 1/4, 1/16, 1/16, 5/16, 1/8] 4 {} {27, 32, 36, 40} {33, 34, 37, 41} {38, 39, 45} [1/4, 1/8, 0, 1/8, 1/8, 3/8, 1/8] 4 {} {27, 35, 36, 37} {33, 34, 40, 41 } {38, 39, 45} [3/16, 1/16, 1/2, 1/16, 1/8, 1/16, 1/16] 4 {} {26, 27, 41} {32, 33, 34 , 40} {37, 38, 39, 45} [3/16, 1/8, 1/2, 1/16, 1/16, 1/16, 1/8] 4 {} {26, 27, 36, 40} {32, 33, 34, 41} {37, 38, 39, 45} [3/8, 1/8, 0, 1/4, 1/8, 1/8, 1/8] 4 {} {26, 27, 35, 36} {33, 34, 40, 41 } {32, 39, 45} [3/8, 1/4, 1/8, 1/8, 1/8, 1/8, 1/8] 4 {} {20, 27, 35, 36} {26, 34, 40, 41} {32, 33, 45} [1/2, 3/8, 1/8, 0, 1/4, 0, 1/8] 3 {} {27, 41} {20, 34, 40} {26, 45} [1/2, 1/8, 1/8, 1/8, 1/8, 1/8, 1/4] 3 {} {20, 21, 36, 40} {26, 27, 41} {32, 33, 34, 45} [1/8, 1/8, 9/32, 1/16, 1/16, 9/32, 3/16] 4 {} {30, 31, 32, 33, 40} {34 , 36, 37, 38} {39, 41, 42, 43} [1/16, 1/16, 5/16, 1/16, 1/8, 1/4, 3/16] 4 {} {30, 31, 38} {34, 36, 37 , 40} {39, 41, 42, 43} [1/8, 1/8, 1/8, 1/8, 1/8, 1/4, 1/4] 4 {} {30, 31, 33, 35, 37} {34, 36, 38, 40} {39, 41, 42, 43} [1/8, 3/16, 1/16, 1/4, 1/16, 1/16, 7/16] 4 {} {31, 32, 33, 40} {30, 34 , 37, 38} {36, 42, 43} [1/16, 3/16, 1/8, 3/16, 1/8, 1/16, 7/16] 4 {} {31, 38} {30, 34, 37, 40} {36, 42, 43} [1/4, 1/8, 1/8, 1/8, 1/8, 1/8, 1/2] 4 {} {25, 32, 33, 40} {30, 31, 37, 38} {34, 36, 42, 43} [1/8, 1/3, 5/24, 1/16, 0, 13/48, 1/3] 4 {} {27, 31, 32, 40} {30, 33, 34 , 37} {36, 38} [1/4, 3/8, 1/8, 0, 1/8, 1/4, 1/4] 4 {} {27, 31, 32, 35} {30, 34, 37, 40 } {33, 36} [1/4, 1/6, 1/6, 1/8, 0, 7/24, 5/12] 4 {} {25, 27, 32, 40} {30, 31, 33, 37} {34, 36, 38} [13/32, 9/32, 5/32, 0, 0, 7/16, 9/32] 3 {} {31, 32, 40} {27, 30, 37} {33, 34, 36} [1/4, 1/4, 1/4, 1/8, 0, 1/8, 1/4] 4 {} {26, 27, 30, 31, 40} {32, 33, 34 , 36} {37, 38, 39, 41} [3/16, 3/16, 7/16, 1/16, 1/16, 1/8, 1/8] 4 {} {26, 27, 30, 31, 35} {32 , 34, 36, 40} {33, 37, 41} [3/8, 1/8, 1/4, 1/8, 0, 1/4, 1/4] 3 {} {26, 30, 31, 40} {27, 32, 36} {33, 34, 37, 41} [1/8, 3/16, 1/2, 1/16, 1/16, 1/16, 3/16] 4 {} {26, 27, 30, 31, 35} {32 , 33, 34, 40} {36, 37, 38} [1/4, 3/8, 3/8, 0, 1/8, 0, 1/4] 3 {} {27, 30, 31, 35} {20, 34, 40} { 26, 36} [1/4, 1/8, 3/8, 1/8, 0, 1/8, 3/8] 3 {} {26, 27, 30, 40} {31, 32, 33} {34, 36, 37, 38} [1/8, 3/16, 1/16, 1/16, 7/16, 3/16, 1/8] 4 {} {27, 29, 31, 32} {30, 34 , 35, 37} {33, 36, 40} [1/16, 1/8, 1/16, 1/8, 7/16, 3/16, 1/8] 4 {} {27, 29, 31, 32} {30, 33, 34, 37} {35, 36} [1/8, 1/4, 1/8, 1/8, 1/8, 3/8, 1/8] 4 {} {23, 27, 31, 32} {29, 30, 34, 37} {33, 35, 36} [1/8, 1/8, 1/8, 1/4, 0, 3/8, 1/4] 4 {} {25, 27, 29, 32} {30, 31, 33, 37 } {34, 35, 36} [3/16, 1/8, 1/16, 1/8, 5/16, 5/16, 1/8] 3 {} {29, 31, 32} {27, 30, 37} {33, 34, 35, 36} [1/4, 1/4, 1/8, 1/8, 1/8, 1/4, 1/8] 4 {} {26, 27, 28, 29, 30, 31} {32, 34, 35, 36} {33, 37, 40, 41} [1/8, 1/8, 1/4, 1/4, 0, 1/4, 1/8] 4 {} {26, 27, 28, 29, 30, 31} {32, 33 , 34, 36} {35, 37, 39} [1/4, 1/8, 1/8, 1/4, 0, 3/8, 1/8] 3 {} {26, 28, 29, 30, 31} {27, 32, 36 } {33, 34, 35, 37} [1/8, 1/4, 1/4, 1/8, 1/8, 1/8, 1/4] 4 {} {26, 27, 28, 29, 30, 31} {32, 33, 34, 35} {36, 37, 38, 40} [1/8, 3/16, 9/16, 1/16, 1/16, 1/16, 1/8] 3 {} {20, 27, 28, 29, 30, 31} {26, 34, 35} {32, 33, 36, 40} [1/8, 1/4, 1/4, 1/4, 0, 1/8, 1/4] 3 {} {26, 27, 29, 30, 31} {28, 33, 34 } {32, 35, 36} [1/8, 1/4, 3/8, 1/8, 0, 1/4, 1/8] 3 {} {26, 27, 28, 30, 31} {29, 32, 34 } {33, 35, 36, 37} [1/8, 1/8, 1/4, 1/4, 0, 1/4, 1/4] 3 {} {26, 27, 28, 29, 30} {31, 32, 33 } {34, 35, 36, 37} [1/8, 1/8, 1/8, 1/8, 1/2, 1/8, 1/8] 6 {} {20, 21, 22, 23, 24, 25} {26, 27, 28, 29, 30, 31} {32, 33, 34, 35, 36} [9/32, 9/32, 9/32, 5/32, 1/8, 5/32, 9/32] 6 {} {21, 22, 23, 24, 25} {20 , 27, 28, 29, 30, 31} {26, 34, 35, 36} [3/8, 1/4, 1/4, 1/8, 1/4, 1/8, 1/4] 6 {} {14, 22, 23, 24, 25} {20, 21, 28, 29, 30, 31} {26, 27, 35, 36} [1, 1/8, 5/8, 1/8, 0, 1/8, 1/8] 4 {} {22, 24, 30} {1, 28, 29, 31} {8 , 35, 36} [3/8, 1/4, 1/4, 1/8, 1/4, 3/8, 3/8] 6 {} {13, 14, 18, 22} {19, 20, 21, 23, 24, 28} {25, 26, 27, 29} [3/8, 1/4, 1/4, 1/8, 1/4, 3/8, 5/8] 6 {} {7, 14, 18, 22} {13, 20, 21, 23, 24, 28} {19, 26, 27, 29} [1/2, 1/4, 1/4, 0, 1/4, 1/2, 1] 5 {} {14, 18, 28} {7, 20, 21, 23, 24} {13, 26, 27, 29} [1/2, 1/4, 0, 1/4, 1/4, 3/4, 1/4] 5 {} {6, 7, 14, 22} {12, 13, 20, 21, 28} {18, 19, 26} [1/4, 1/4, 1/4, 1/4, 1/4, 1/4, 1/4] 6 {} {14, 15, 16, 17, 18, 19} {20, 21, 22, 23, 24, 25} {26, 27, 28, 29, 30, 31} [1/4, 1/4, 1/4, 1/4, 1/4, 1/4, 3/4] 6 {} {7, 14, 15, 16, 17, 18} {13, 20, 21, 22, 23, 24} {19, 26, 27, 28, 29} [1/8, 1/4, 1/4, 3/8, 1/4, 1/8, 1] 5 {} {14, 15, 16, 17, 18} {7, 20, 21 , 23, 24} {13, 22, 27} [1/4, 1/2, 1/4, 0, 1/2, 1/4, 3/4] 5 {} {7, 14, 15, 17, 18} {13, 16, 20 , 21, 24} {19, 22, 23, 27} [1, 1/4, 3/4, 0, 1/4, 1/2, 1/2] 5 {} {7, 10, 16, 18} {1, 13, 15, 17, 23 } {8, 19, 22, 24} [1/4, 1/4, 1/4, 1/4, 1/4, 1/2, 1/2] 5 {} {7, 12, 14, 15, 16, 17} {13, 18, 20, 21, 22} {19, 23, 24, 26, 28} [1, 1/4, 1/2, 1/4, 1/4, 1/2, 1/4] 5 {} {10, 12, 13, 16} {1, 15, 17, 18 , 19} {8, 22, 23, 24, 25} [5/8, 3/8, 3/8, 1/4, 3/8, 3/8, 5/8] 6 {} {1, 7, 9, 10, 11, 12} {8, 13, 15, 16, 17, 18} {14, 19, 22, 23, 24} [1/4, 1/4, 1/4, 1/2, 1/4, 3/4, 1/4] 6 {} {6, 7, 8, 9, 10, 11} {12, 13, 14, 15, 16, 17} {18, 19, 20, 21, 22} [1, 1/4, 1/4, 1/2, 1/4, 1, 1] 6 {} {9, 10, 11} {1, 6, 7, 15, 16, 17} {8, 12, 13, 22} [1, 1/4, 1, 3/4, 1/4, 3/4, 1/4] 6 {} {2, 4, 5, 6, 7} {1, 3, 9, 11, 12, 13} {8, 10, 16, 18, 19} [1, 1, 1, 1, 1, 1, 1] 7 {} {} {1, 2, 3, 4, 5, 6, 7} {8, 9, 10, 11, 12 , 13} [5/8, 3/8, 3/8, 0, 1/4, 3/8, 3/8] 6 {4} {1, 12, 13, 15, 16, 17} {8, 19 , 22, 23, 24} {20, 21, 29, 30, 31} [1, 1, 1, 0, 1, 1, 1] 7 {4} {} {1, 2, 3, 5, 6, 7} {8, 12, 13, 15, 16 , 17} [1/4, 1/4, 1/4, 1/2, 0, 1/4, 3/4] 6 {5} {7, 8, 9, 10, 18} {13, 14, 15, 23, 24} {20, 25, 27, 28, 29} [5/8, 0, 0, 3/8, 0, 5/8, 0] 6 {2, 3, 5, 7} {1, 6, 28} {14, 18} {27, 32, 35} [1, 0, 0, 1, 0, 1, 0] 7 {2, 3, 5, 7} {} {1, 4, 6} {14, 18, 28}