Unipotent representations for G = E7, adjoint, hermitian G^v = E7, simply connected, split Atlas version 0.3./Build date: Nov 19 2007 at 06:09:46. Unipotent representations computed from file orbitsAndCells_E7_ad_s_1_3 at Thu Dec 4 10:44:45 2008 Note: 4 orbits have the wrong infinitesimal character and are excluded. See the orbits and cells file. O^v diagram(O^v) O cell Unipotent representations E7 2222222 1 16 1980 15 1979 E7(a1) 2220222 A1 14 1947 E7(a2) 2220202 2A1 10 1436 13 1932 12 1933 E7(a3) 2002022 A2 11 1822,1823 Number of orbits: 7 Number of even orbits: 4 Number of cells: 7 Number of unipotent representations: 8 All unipotent parameters/duals: Unipotent Dual 1436 544 1822 157 1823 158 1932 47 1933 48 1947 33 1979 0 1980 1 Unipotent representations from block file: 1436(1267,15540): 15 2 [ic,C-,ic,C+,C-,C+,r1] 1436 1311 1436 1522 1332 1535 1436 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (1372,1374) 2,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 1822(1558,10071): 20 3 [C-,C+,C+,C-,C+,ic,ic] 1741 1876 1876 1771 1870 1822 1822 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,1,4,3,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1823(1558,10072): 20 3 [C-,C+,C+,C-,C+,ic,ic] 1740 1877 1877 1770 1871 1823 1823 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,1,4,3,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1932(1635, 6654): 23 3 [ic,C-,ic,C+,C-,C+,C-] 1932 1893 1932 1949 1902 1955 1900 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1933(1635, 6655): 23 3 [ic,C-,ic,C+,C-,C+,C-] 1933 1892 1933 1948 1903 1954 1901 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1947(1645, 6543): 23 2 [C-,C-,C-,C+,ic,ic,C-] 1919 1921 1922 1963 1947 1947 1923 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,5,4,2,3,1,6,5,4,2,3,1,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3 1979(1665, 2853): 27 3 [C-,ic,ic,ic,ic,C-,r2] 1974 1979 1979 1979 1979 1976 1980 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (1978, *) 1,3,4,2,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1980(1665, 2854): 27 3 [C-,ic,ic,ic,ic,C-,r2] 1975 1980 1980 1980 1980 1977 1979 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (1978, *) 1,3,4,2,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 Dual to unipotent representations from dual block: 544(15540,1267): 20 7 [rn,C+,rn,C-,C+,C-,i2] 544 669 544 458 648 445 544 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 609, 611) 1,3,1,4,2,3,1,4,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 157(10071,1558): 15 5 [C+,C-,C-,C+,C-,rn,rn] 240 103 103 210 109 157 157 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,4,5,6,7 158(10072,1558): 15 5 [C+,C-,C-,C+,C-,rn,rn] 239 104 104 209 110 158 158 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,4,5,6,7 47( 6654,1635): 12 5 [rn,C+,rn,C-,C+,C-,C+] 47 88 47 32 77 26 79 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,6 48( 6655,1635): 12 5 [rn,C+,rn,C-,C+,C-,C+] 48 87 48 31 78 25 80 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,6 33( 6543,1645): 12 7 [C+,C+,C+,C-,rn,rn,C+] 61 59 58 17 33 33 57 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,5,4,2,3,4,6,5,4,2,3,4,5,7,6,5,4 0( 2853,1665): 8 5 [C+,rn,rn,rn,rn,C+,i1] 5 0 0 0 0 3 1 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 2, *) 2,3,4,2,3,4,5,4,2,3,4,5 1( 2854,1665): 8 5 [C+,rn,rn,rn,rn,C+,i1] 6 1 1 1 1 4 0 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 2, *) 2,3,4,2,3,4,5,4,2,3,4,5