/usr/share/gap/pkg/ctbllib/dlnames/uctypeX.g is in gap-character-tables 1r2p2.dfsg.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 | #############################################################################
##
#W uctypeX.g GAP 4 package CTblLib Michael Claßen-Houben
##
#Y Copyright (C) 2005, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
##
## This file contains Deligne-Lusztig names of $^3D$, $E$, $^2E$, $F$, $G$,
## $^b$, $^2F$, and $^G$ type groups.
##
Append( DeltigLibUnipotentCharacters, [
rec( isoc := "3D", l := 4, q := 2, isot := [ "ad", "sc", "simple" ],
identifier := "3D4(2)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,3}'", index := 2 ),
rec( label := "phi{2,2}", index := 10 ),
rec( label := "phi{2,1}", index := 6 ),
rec( label := "phi{1,3}''", index := 14 ),
rec( label := "phi{1,6}", index := 34 ),
rec( label := "^3D_4[-1]", index := 4 ),
rec( label := "^3D_4[1]", index := 3 ) ] ),
rec( isoc := "E", l := 6, q := 2, isot := [ "ad", "sc", "simple" ],
identifier := "E6(2)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{6,1}", index := 2 ),
rec( label := "phi{20,2}", index := 3 ),
rec( label := "phi{64,4}", index := 11 ),
rec( label := "phi{60,5}", index := 16 ),
rec( label := "phi{81,6}", index := 21 ),
rec( label := "phi{24,6}", index := 13 ),
rec( label := "phi{81,10}", index := 48 ),
rec( label := "phi{60,11}", index := 55 ),
rec( label := "phi{24,12}", index := 37 ),
rec( label := "phi{64,13}", index := 74 ),
rec( label := "phi{20,20}", index := 131 ),
rec( label := "phi{6,25}", index := 134 ),
rec( label := "phi{1,36}", index := 174 ),
rec( label := "phi{30,3}", index := 8 ),
rec( label := "phi{15,5}", index := 5 ),
rec( label := "phi{15,4}", index := 7 ),
rec( label := "D_4,1", index := 4 ),
rec( label := "phi{30,15}", index := 77 ),
rec( label := "phi{15,17}", index := 58 ),
rec( label := "phi{15,16}", index := 68 ),
rec( label := "D_4,eps", index := 41 ),
rec( label := "phi{80,7}", index := 30 ),
rec( label := "phi{20,10}", index := 20 ),
rec( label := "phi{60,8}", index := 29 ),
rec( label := "phi{10,9}", index := 22 ),
rec( label := "phi{90,8}", index := 31 ),
rec( label := "D_4,r", index := 18 ),
rec( label := "E_6[theta]", index := 14 ),
rec( label := "E_6[theta^2]", index := 15 ) ] ),
rec( isoc := "2E", l := 6, q := 2, isot := [ "ad" ],
identifier := "2E6(2).3",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,12}''", index := 111 ),
rec( label := "phi{1,12}'", index := 10 ),
rec( label := "phi{1,24}", index := 259 ),
rec( label := "phi{2,4}''", index := 13 ),
rec( label := "phi{2,16}'", index := 121 ),
rec( label := "phi{2,4}'", index := 4 ),
rec( label := "phi{2,16}''", index := 199 ),
rec( label := "phi{4,8}", index := 54 ),
rec( label := "phi{9,2}", index := 22 ),
rec( label := "phi{9,6}''", index := 95 ),
rec( label := "phi{9,6}'", index := 41 ),
rec( label := "phi{9,10}", index := 144 ),
rec( label := "phi{6,6}'", index := 61 ),
rec( label := "phi{6,6}''", index := 44 ),
rec( label := "phi{12,4}", index := 58 ),
rec( label := "phi{4,1}", index := 7 ),
rec( label := "phi{4,7}''", index := 105 ),
rec( label := "phi{4,7}'", index := 35 ),
rec( label := "phi{4,13}", index := 162 ),
rec( label := "phi{8,3}''", index := 32 ),
rec( label := "phi{8,9}'", index := 98 ),
rec( label := "phi{8,3}'", index := 19 ),
rec( label := "phi{8,9}''", index := 137 ),
rec( label := "phi{16,5}", index := 71 ),
rec( label := "2A_5[1]", index := 28 ),
rec( label := "2A_5[eps]", index := 108 ),
rec( label := "2E_6[1]", index := 25 ),
rec( label := "2E_6[theta]", index := 47 ),
rec( label := "2E_6[theta^2]", index := 50 ) ] ),
rec( isoc := "2E", l := 6, q := 2, isot := [ "simple" ],
identifier := "2E6(2)", labelingfrom := "2E6(2).3" ),
rec( isoc := "F", l := 4, q := 2, isot := [ "ad", "sc", "simple" ],
identifier := "F4(2)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,12}''", index := 14 ),
rec( label := "phi{1,12}'", index := 15 ),
rec( label := "phi{1,24}", index := 94 ),
rec( label := "phi{2,4}''", index := 3 ),
rec( label := "phi{2,16}'", index := 68 ),
rec( label := "phi{2,4}'", index := 4 ),
rec( label := "phi{2,16}''", index := 67 ),
rec( label := "phi{4,8}", index := 27 ),
rec( label := "phi{9,2}", index := 8 ),
rec( label := "phi{9,6}''", index := 33 ),
rec( label := "phi{9,6}'", index := 34 ),
rec( label := "phi{9,10}", index := 72 ),
rec( label := "phi{6,6}'", index := 32 ),
rec( label := "phi{6,6}''", index := 24 ),
rec( label := "phi{12,4}", index := 37 ),
rec( label := "phi{4,1}", index := 6 ),
rec( label := "phi{4,7}''", index := 30 ),
rec( label := "phi{4,7}'", index := 31 ),
rec( label := "phi{4,13}", index := 71 ),
rec( label := "phi{8,3}''", index := 11 ),
rec( label := "phi{8,9}'", index := 57 ),
rec( label := "phi{8,3}'", index := 12 ),
rec( label := "phi{8,9}''", index := 56 ),
rec( label := "phi{16,5}", index := 44 ),
rec( label := "[ [ 2 ], [ ] ]", index := 2 ),
rec( label := "[ [ ], [ 1, 1 ] ]", index := 58 ),
rec( label := "[ [ 1 ], [ 1 ] ]", index := 25 ),
rec( label := "[ [ ], [ 2 ] ]", index := 22 ),
rec( label := "[ [ 1, 1 ], [ ] ]", index := 23 ),
rec( label := "F4[theta]", index := 20 ),
rec( label := "F4[theta^2]", index := 21 ),
rec( label := "F4[i]", index := 16 ),
rec( label := "F4[-i]", index := 17 ),
rec( label := "F4^I[1]", index := 7 ),
rec( label := "F4^II[1]", index := 5 ),
rec( label := "F4[-1]", index := 13 ) ] ),
rec( isoc := "G", l := 2, q := 2, isot := [ "ad", "sc", "simple" ],
identifier := "U3(3).2",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,6}", index := 16 ),
rec( label := "phi{1,3}'", index := 7 ),
rec( label := "phi{1,3}''", index := 8 ),
rec( label := "phi{2,1}", index := 10 ),
rec( label := "phi{2,2}", index := 13 ),
rec( label := "G2[1]", index := 2 ),
rec( label := "G2[-1]", index := 5, warn := true ),
rec( label := "G2[theta]", index := 3 ),
rec( label := "G2[theta^2]", index := 4 ) ] ),
rec( isoc := "G", l := 2, q := 3, isot := [ "ad", "sc", "simple" ],
identifier := "G2(3)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,6}", index := 21 ),
rec( label := "phi{1,3}'", index := 7 ),
rec( label := "phi{1,3}''", index := 8 ),
rec( label := "phi{2,1}", index := 9 ),
rec( label := "phi{2,2}", index := 10 ),
rec( label := "G2[1]", index := 2 ),
rec( label := "G2[-1]", index := 5 ),
rec( label := "G2[theta]", index := 3 ),
rec( label := "G2[theta^2]", index := 4 ) ] ),
rec( isoc := "G", l := 2, q := 4, isot := [ "ad", "sc", "simple" ],
identifier := "G2(4)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,6}", index := 28 ),
rec( label := "phi{1,3}'", index := 7 ),
rec( label := "phi{1,3}''", index := 8 ),
rec( label := "phi{2,1}", index := 6 ),
rec( label := "phi{2,2}", index := 10 ),
rec( label := "G2[1]", index := 3 ),
rec( label := "G2[-1]", index := 9 ),
rec( label := "G2[theta]", index := 4 ),
rec( label := "G2[theta^2]", index := 5 ) ] ),
rec( isoc := "G", l := 2, q := 5, isot := [ "ad", "sc", "simple" ],
identifier := "G2(5)",
labeling := [ rec( label := "phi{1,0}", index := 1 ),
rec( label := "phi{1,6}", index := 38 ),
rec( label := "phi{1,3}'", index := 8 ),
rec( label := "phi{1,3}''", index := 9 ),
rec( label := "phi{2,1}", index := 5 ),
rec( label := "phi{2,2}", index := 11 ),
rec( label := "G2[1]", index := 3 ),
rec( label := "G2[-1]", index := 10 ),
rec( label := "G2[theta]", index := 6 ),
rec( label := "G2[theta^2]", index := 7 ) ] ),
rec( isoc := "2B", l := 2, q2 := 2, isot := [ "ad", "sc", "simple" ],
identifier := "5:4",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps", index := 5 ),
rec( label := "^2B_2[a],1", index := 2, warn := true ),
rec( label := "^2B_2[b],1", index := 4, warn := true ) ] ),
rec( isoc := "2B", l := 2, q2 := 8, isot := [ "ad", "sc", "simple" ],
identifier := "Sz(8)",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps", index := 7 ),
rec( label := "^2B_2[a],1", index := 2 ),
rec( label := "^2B_2[b],1", index := 3 ) ] ),
rec( isoc := "2B", l := 2, q2 := 32, isot := [ "ad", "sc", "simple" ],
identifier := "Sz(32)",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps", index := 14 ),
rec( label := "^2B_2[a],1", index := 2 ),
rec( label := "^2B_2[b],1", index := 3 ) ] ),
rec( isoc := "2G", l := 2, q2 := 3, isot := [ "ad", "sc", "simple" ],
identifier := "L2(8).3",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps", index := 11 ),
rec( label := "cusp1", index := 9 ),
rec( label := "cusp2", index := 10 ),
rec( label := "cusp3", index := 2 ),
rec( label := "cusp4", index := 3 ),
rec( label := "cusp5", index := 5 ),
rec( label := "cusp6", index := 6 ) ] ),
rec( isoc := "2G", l := 2, q2 := 27, isot := [ "ad", "sc", "simple" ],
identifier := "R(27)",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps", index := 20 ),
rec( label := "cusp1", index := 7 ),
rec( label := "cusp2", index := 8 ),
rec( label := "cusp3", index := 3 ),
rec( label := "cusp4", index := 4 ),
rec( label := "cusp5", index := 5 ),
rec( label := "cusp6", index := 6 ) ] ),
rec( isoc := "2F", l := 4, q2 := 2, isot := [ "ad", "sc", "simple" ],
identifier := "2F4(2)'.2",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps'", index := 8 ),
rec( label := "eps''", index := 20 ),
rec( label := "eps", index := 29 ),
rec( label := "rho_2'", index := 14 ),
rec( label := "rho_2''", index := 23 ),
rec( label := "rho_2", index := 21 ),
rec( label := "^2B_2[a],1", index := 4 ),
rec( label := "^2B_2[b],1", index := 5 ),
rec( label := "^2B_2[a],eps", index := 28 ),
rec( label := "^2B_2[b],eps", index := 27 ),
rec( label := "cusp1", index := 12 ),
rec( label := "cusp2", index := 2 ),
rec( label := "cusp3", index := 9 ),
rec( label := "cusp4", index := 6 ),
rec( label := "cusp5", index := 7 ),
rec( label := "cusp6", index := 16 ),
rec( label := "cusp7", index := 18 ),
rec( label := "cusp8", index := 10 ),
rec( label := "cusp9", index := 11 ),
rec( label := "cusp10", index := 3 ) ] ),
rec( isoc := "2F", l := 4, q2 := 8, isot := [ "ad", "sc", "simple" ],
identifier := "2F4(8)",
labeling := [ rec( label := "1", index := 1 ),
rec( label := "eps'", index := 4 ),
rec( label := "eps''", index := 30 ),
rec( label := "eps", index := 100 ),
rec( label := "rho_2'", index := 10 ),
rec( label := "rho_2''", index := 17 ),
rec( label := "rho_2", index := 18 ),
rec( label := "^2B_2[a],1", index := 2 ),
rec( label := "^2B_2[b],1", index := 3 ),
rec( label := "^2B_2[a],eps", index := 40 ),
rec( label := "^2B_2[b],eps", index := 41 ),
rec( label := "cusp1", index := 12 ),
rec( label := "cusp2", index := 5 ),
rec( label := "cusp3", index := 9 ),
rec( label := "cusp4", index := 7 ),
rec( label := "cusp5", index := 8 ),
rec( label := "cusp6", index := 15 ),
rec( label := "cusp7", index := 16 ),
rec( label := "cusp8", index := 13 ),
rec( label := "cusp9", index := 14 ),
rec( label := "cusp10", index := 11 ) ] )
] );
#############################################################################
##
#E
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