Computing weak packets for 21 dual orbits of connected real group with Lie algebra 'e6(f4)' Initializing CharacterTable for Lie type 'E6' Step 1/6 Step 2/6 Step 3/6 Step 4/6 Step 5/6 Step 6/6 Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 2, 2, 2, 2, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 0, 0, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 2, 2, 0, 2, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 1, 2, 2, 3, 2, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 2, 0, 2, 0, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 2, 2, 3, 4, 3, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 2, 0, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 2, 3, 4, 6, 4, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 2, 0, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 2, 4, 4, 6, 4, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 2, 1, 0, 1, 1 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 3, 4, 5, 7, 5, 3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 2, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 4, 4, 6, 8, 6, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 1, 1, 0, 1, 1 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 3, 4, 6, 8, 6, 3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 2, 0, 0, 0, 2 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 4, 6, 7, 10, 7, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 2, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 4, 5, 7, 10, 7, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 2, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 4, 6, 8, 11, 8, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 2, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 4, 6, 8, 12, 8, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 2, 0, 0, 0, 1 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 6, 8, 10, 14, 10, 6 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 0, 0, 2 ]) Computing weak packet for orbit: simply connected root datum of Lie type 'E6' [ 6, 10, 12, 18, 12, 6 ] dim=60 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 19, 27, 36, 51, 36, 19 ]/1 gamma_final:[ 3, 5, 6, 9, 6, 3 ]/1 Initializing CharacterTable for Lie type 'E6' Step 1/6 Step 2/6 Step 3/6 Step 4/6 Step 5/6 Step 6/6 integral data: st_int rd_int:adjoint root datum of Lie type 'E6' st_int.rd: simply connected root datum of Lie type 'E6' O_check_int:(adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 2, 0, 0 ]) computing packet for:(adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 2, 0, 0 ]) computing springer map of[2,0,0,0,0,2] O: (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 0, 0, 2 ]) survive:final parameter(x=0,lambda=[19,27,36,51,36,19]/1,nu=[0,0,0,0,0,0]/1) [ 3, 5, 6, 9, 6, 3 ]/1 cell character: 13 springer_O:13 dim: 20 24 dim: 1 24 Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 0, 0, 1, 0, 1 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 6, 8, 11, 15, 11, 6 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 1, 0, 0, 0, 1 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 7, 10, 13, 18, 13, 7 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 0, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 8, 10, 14, 19, 14, 8 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 0, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 8, 10, 14, 20, 14, 8 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 1, 0, 0, 0, 0, 1 ]) Computing weak packet for orbit: simply connected root datum of Lie type 'E6' [ 10, 14, 18, 26, 18, 10 ] dim=68 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 21, 29, 39, 55, 39, 21 ]/1 gamma_final:[ 5, 7, 9, 13, 9, 5 ]/1 Initializing CharacterTable for Lie type 'E6' Step 1/6 Step 2/6 Step 3/6 Step 4/6 Step 5/6 Step 6/6 integral data: st_int rd_int:adjoint root datum of Lie type 'E6' st_int.rd: simply connected root datum of Lie type 'E6' O_check_int:(adjoint root datum of Lie type 'E6',(),[ 2, 2, 0, 2, 0, 2 ]) computing packet for:(adjoint root datum of Lie type 'E6',(),[ 2, 2, 0, 2, 0, 2 ]) computing springer map of[1,0,0,0,0,1] O: (adjoint root datum of Lie type 'E6',(),[ 1, 0, 0, 0, 0, 1 ]) survive:final parameter(x=0,lambda=[21,29,39,55,39,21]/1,nu=[0,0,0,0,0,0]/1) [ 5, 7, 9, 13, 9, 5 ]/1 survive:final parameter(x=2,lambda=[20,29,39,55,39,20]/1,nu=[3,0,0,0,0,3]/2) [ 5, 7, 9, 13, 9, 5 ]/1 survive:final parameter(x=13,lambda=[18,29,36,49,36,18]/1,nu=[4,0,4,8,4,4]/1) [ 5, 7, 9, 13, 9, 5 ]/1 survive:final parameter(x=19,lambda=[17,21,35,47,35,17]/1,nu=[11,22,11,22,11,11]/2) [ 5, 7, 9, 13, 9, 5 ]/1 survive:final parameter(x=31,lambda=[16,19,29,35,29,16]/1,nu=[8,16,16,32,16,8]/1) [ 5, 7, 9, 13, 9, 5 ]/1 cell character: 10 springer_O:10 dim: 1 20 Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 1, 0, 0, 0, 0 ]) Skipping dual orbit (simply connected root datum of Lie type 'E6',(),[ 12, 16, 22, 30, 22, 12 ]) (d(O_check) has no real forms for G) Orbit by diagram: (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 0, 0, 0 ]) Computing weak packet for orbit: simply connected root datum of Lie type 'E6' [ 16, 22, 30, 42, 30, 16 ] dim=72 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 24, 33, 45, 63, 45, 24 ]/1 gamma_final:[ 8, 11, 15, 21, 15, 8 ]/1 Initializing CharacterTable for Lie type 'E6' Step 1/6 Step 2/6 Step 3/6 Step 4/6 Step 5/6 Step 6/6 integral data: st_int rd_int:adjoint root datum of Lie type 'E6' st_int.rd: simply connected root datum of Lie type 'E6' O_check_int:(adjoint root datum of Lie type 'E6',(),[ 2, 2, 2, 2, 2, 2 ]) computing packet for:(adjoint root datum of Lie type 'E6',(),[ 2, 2, 2, 2, 2, 2 ]) computing springer map of[0,0,0,0,0,0] O: (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 0, 0, 0 ]) survive:final parameter(x=0,lambda=[24,33,45,63,45,24]/1,nu=[0,0,0,0,0,0]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=1,lambda=[24,33,44,63,44,24]/1,nu=[0,0,3,0,3,0]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=2,lambda=[23,33,45,63,45,23]/1,nu=[3,0,0,0,0,3]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=3,lambda=[24,33,43,59,43,24]/1,nu=[0,0,3,6,3,0]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=4,lambda=[23,33,43,63,44,22]/1,nu=[3,0,6,0,3,6]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=5,lambda=[22,33,44,63,43,23]/1,nu=[6,0,3,0,6,3]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=6,lambda=[23,33,42,58,43,21]/1,nu=[3,0,9,15,6,9]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=7,lambda=[24,27,42,57,42,24]/1,nu=[0,18,9,18,9,0]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=8,lambda=[21,33,43,58,42,23]/1,nu=[9,0,6,15,9,3]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=9,lambda=[22,33,43,63,43,22]/1,nu=[3,0,3,0,3,3]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=10,lambda=[22,33,41,57,37,20]/1,nu=[3,0,6,9,12,6]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=11,lambda=[20,33,37,57,41,22]/1,nu=[6,0,12,9,6,3]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=12,lambda=[23,26,41,56,42,20]/1,nu=[3,21,12,21,9,12]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=13,lambda=[21,33,42,57,42,21]/1,nu=[9,0,9,18,9,9]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=14,lambda=[20,26,42,56,41,23]/1,nu=[12,21,9,21,12,3]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=15,lambda=[20,33,37,56,41,21]/1,nu=[12,0,24,21,12,9]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=16,lambda=[22,25,40,55,35,19]/1,nu=[6,24,15,24,30,15]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=17,lambda=[19,25,35,55,40,22]/1,nu=[15,24,30,24,15,6]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=18,lambda=[21,33,41,56,37,20]/1,nu=[9,0,12,21,24,12]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=19,lambda=[20,25,41,55,41,20]/1,nu=[6,12,6,12,6,6]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=20,lambda=[21,24,39,45,33,18]/1,nu=[9,27,18,54,36,18]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=21,lambda=[18,24,33,45,39,21]/1,nu=[18,27,36,54,18,9]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=23,lambda=[19,24,35,54,40,20]/1,nu=[15,27,30,27,15,12]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=24,lambda=[20,24,40,54,35,19]/1,nu=[12,27,15,27,30,15]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=22,lambda=[20,33,37,55,37,20]/1,nu=[6,0,12,12,12,6]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=25,lambda=[17,23,31,42,27,20]/1,nu=[21,30,42,63,54,12]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=26,lambda=[20,23,27,42,31,17]/1,nu=[12,30,54,63,42,21]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=27,lambda=[18,23,33,45,39,20]/1,nu=[9,15,18,27,9,6]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=28,lambda=[19,23,35,53,35,19]/1,nu=[15,30,30,30,30,15]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=29,lambda=[20,23,39,45,33,18]/1,nu=[6,15,9,27,18,9]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=30,lambda=[16,21,29,39,25,8]/1,nu=[12,18,24,36,30,24]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=31,lambda=[18,21,33,39,33,18]/1,nu=[9,18,18,36,18,9]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=32,lambda=[17,21,31,42,26,19]/1,nu=[21,36,42,63,57,15]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=33,lambda=[19,21,26,42,31,17]/1,nu=[15,36,57,63,42,21]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=34,lambda=[8,21,25,39,29,16]/1,nu=[24,18,30,36,24,12]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=35,lambda=[17,20,31,37,25,18]/1,nu=[21,39,42,78,60,18]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=36,lambda=[18,20,25,37,31,17]/1,nu=[18,39,60,78,42,21]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=37,lambda=[16,20,29,39,24,8]/1,nu=[24,39,48,72,63,48]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=38,lambda=[8,20,24,39,29,16]/1,nu=[48,39,63,72,48,24]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=39,lambda=[16,19,29,35,23,8]/1,nu=[12,21,24,42,33,24]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=40,lambda=[17,19,24,35,24,17]/1,nu=[21,42,63,84,63,21]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=41,lambda=[8,19,23,35,29,16]/1,nu=[24,21,33,42,24,12]/1) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=42,lambda=[16,18,23,33,22,8]/1,nu=[24,45,66,90,69,48]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=43,lambda=[8,18,22,33,23,16]/1,nu=[48,45,69,90,66,24]/2) [ 8, 11, 15, 21, 15, 8 ]/1 survive:final parameter(x=44,lambda=[8,17,21,31,21,8]/1,nu=[24,24,36,48,36,24]/1) [ 8, 11, 15, 21, 15, 8 ]/1 cell character: 1 springer_O:1 Computing weak packets for 16 dual orbits of connected real group with Lie algebra 'so(9,1).gl(1,R)' Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -10, 2, 2, 2, 2, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -7, 2, 2, 0, 2, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 2, 2, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -6, 0, 0, 2, 2, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 2, 2, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -6, 2, 2, 0, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 3, 2, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -4, 0, 0, 2, 0, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 4, 3, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -4, 0, 0, 2, 0, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 4, 4, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -3, 0, 0, 0, 2, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 6, 6, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -4, 1, 1, 0, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 5, 4, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -3, 0, 0, 2, 0, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 6, 4, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -3, 1, 1, 0, 1, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 7, 6, 3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -2, 0, 0, 0, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 7, 6, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -2, 0, 0, 0, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 8, 6, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -1, 0, 0, 0, 0, 2 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ 0, 6, 6, 12, 10, 6 ] dim=36 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 0, 13, 13, 24, 19, 11 ]/1 gamma_final:[ 0, 3, 3, 6, 5, 3 ]/1 integral data: st_int rd_int:root datum of Lie type 'D5.T1' st_int.rd: simply connected root datum of Lie type 'D5' O_check_int:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 0, 0 ]) computing packet for:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 0, 0 ]) computing springer map of[2,0,0,0,0] O: (adjoint root datum of Lie type 'D5',(),[ 2, 0, 0, 0, 0 ]) survive:final parameter(x=0,lambda=[0,13,13,24,19,11]/1,nu=[0,0,0,0,0,0]/1) [ 0, 3, 3, 6, 5, 3 ]/1 cell character: 12 springer_O:12 dim: 1 4 Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -2, 1, 1, 0, 0, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 6, 6, 10, 8, 4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ -1, 0, 0, 0, 1, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 7, 7, 12, 10, 6 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 0, 0, 0 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ 0, 10, 10, 18, 14, 8 ] dim=40 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 0, 15, 15, 27, 21, 12 ]/1 gamma_final:[ 0, 5, 5, 9, 7, 4 ]/1 integral data: st_int rd_int:root datum of Lie type 'D5.T1' st_int.rd: simply connected root datum of Lie type 'D5' O_check_int:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 2, 2 ]) computing packet for:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 2, 2 ]) computing springer map of[0,0,0,0,0] O: (adjoint root datum of Lie type 'D5',(),[ 0, 0, 0, 0, 0 ]) survive:final parameter(x=0,lambda=[0,15,15,27,21,12]/1,nu=[0,0,0,0,0,0]/1) [ 0, 5, 5, 9, 7, 4 ]/1 survive:final parameter(x=1,lambda=[0,14,14,27,21,12]/1,nu=[0,3,3,0,0,0]/2) [ 0, 5, 5, 9, 7, 4 ]/1 survive:final parameter(x=2,lambda=[0,13,13,23,21,12]/1,nu=[0,3,3,6,0,0]/1) [ 0, 5, 5, 9, 7, 4 ]/1 survive:final parameter(x=3,lambda=[0,12,12,21,15,12]/1,nu=[0,9,9,18,18,0]/2) [ 0, 5, 5, 9, 7, 4 ]/1 survive:final parameter(x=4,lambda=[0,11,11,19,13,4]/1,nu=[0,6,6,12,12,12]/1) [ 0, 5, 5, 9, 7, 4 ]/1 cell character: 11 springer_O:11 Computing weak packets for 16 dual orbits of connected real group with Lie algebra 'so(9,1).gl(1,R)' Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 2, 2, 2, 2, -10 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 2, 2, 0, 2, -7 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 1, 1, 2, 2, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 0, 2, 2, 0, -6 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 1, 2, 2, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 0, 2, -6 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 1, 2, 2, 3, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 0, 0, 2, 0, -4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 2, 3, 4, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 0, 0, 2, 0, -4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 2, 4, 4, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 1, 2, 0, 1, -4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 3, 4, 5, 3, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 0, 2, 0, 0, -3 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 4, 3, 6, 6, 3, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 2, 0, -3 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 3, 4, 6, 3, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 0, 1, -3 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 3, 4, 6, 7, 4, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 2, 0, 0, -2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 4, 4, 6, 7, 4, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 2, 0, 0, -2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 4, 4, 6, 8, 4, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 1, 0, 0, 1, -2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 4, 6, 8, 10, 6, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 0, 0, 0, 0, -1 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ 6, 6, 10, 12, 6, 0 ] dim=36 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 11, 13, 19, 24, 13, 0 ]/1 gamma_final:[ 3, 3, 5, 6, 3, 0 ]/1 integral data: st_int rd_int:root datum of Lie type 'D5.T1' st_int.rd: simply connected root datum of Lie type 'D5' O_check_int:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 0, 0 ]) computing packet for:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 0, 0 ]) computing springer map of[2,0,0,0,0] O: (adjoint root datum of Lie type 'D5',(),[ 2, 0, 0, 0, 0 ]) survive:final parameter(x=0,lambda=[11,13,19,24,13,0]/1,nu=[0,0,0,0,0,0]/1) [ 3, 3, 5, 6, 3, 0 ]/1 cell character: 12 springer_O:12 dim: 1 4 Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 1, 0, 0, -1 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 6, 7, 10, 12, 7, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 0, 0, 0 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ 8, 10, 14, 18, 10, 0 ] dim=40 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 12, 15, 21, 27, 15, 0 ]/1 gamma_final:[ 4, 5, 7, 9, 5, 0 ]/1 integral data: st_int rd_int:root datum of Lie type 'D5.T1' st_int.rd: simply connected root datum of Lie type 'D5' O_check_int:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 2, 2 ]) computing packet for:(adjoint root datum of Lie type 'D5',(),[ 2, 2, 2, 2, 2 ]) computing springer map of[0,0,0,0,0] O: (adjoint root datum of Lie type 'D5',(),[ 0, 0, 0, 0, 0 ]) survive:final parameter(x=0,lambda=[12,15,21,27,15,0]/1,nu=[0,0,0,0,0,0]/1) [ 4, 5, 7, 9, 5, 0 ]/1 survive:final parameter(x=1,lambda=[12,14,21,27,14,0]/1,nu=[0,3,0,0,3,0]/2) [ 4, 5, 7, 9, 5, 0 ]/1 survive:final parameter(x=2,lambda=[12,13,21,23,13,0]/1,nu=[0,3,0,6,3,0]/1) [ 4, 5, 7, 9, 5, 0 ]/1 survive:final parameter(x=3,lambda=[12,12,15,21,12,0]/1,nu=[0,9,18,18,9,0]/2) [ 4, 5, 7, 9, 5, 0 ]/1 survive:final parameter(x=4,lambda=[4,11,13,19,11,0]/1,nu=[12,6,12,12,6,0]/1) [ 4, 5, 7, 9, 5, 0 ]/1 cell character: 11 springer_O:11 =============================================================================== Orbits for the dual group: connected quasisplit real group with Lie algebra 'e6(su(6).su(2))' complex nilpotent orbits for inner class Complex reductive group of type E6, with involution defining inner class of type 'c', with 3 real forms and 2 dual real forms root datum of inner class: simply connected root datum of Lie type 'E6' i: orbit number H: semisimple element BC Levi: Bala-Carter Levi Cent_0: identity component of Cent(SL(2)) Z(Cent^0): order of center of derived group of id. comp. of Centralizer C_2: conjugacy classes in Cent(SL(2))_0 with square 1 A(O): orders of conj. classes in component group of centralizer of O #RF: number of real forms of O for all real forms (of integrality datum) in inner class #AP: number of Arthur parameters for O i diagram dim BC Levi Cent_0 Z C_2 A(O) #RF #AP 0 [0,0,0,0,0,0] 0 6T1 E6 3 3 [1] [1,1,1] 3 1 [0,1,0,0,0,0] 22 A1+5T1 A5 6 4 [1] [0,0,2,0,2] 4 2 [1,0,0,0,0,1] 32 2A1+4T1 B3+T1 2 5 [1] [0,0,0,0,3,2] 5 3 [0,0,0,1,0,0] 40 3A1+3T1 A1+A2 6 4 [1] [0,0,0,0,4] 4 4 [0,2,0,0,0,0] 42 A2+4T1 2A2 9 4 [1,2] [0,1,3] 4 5 [1,1,0,0,0,1] 46 A1+A2+3T1 A2+T1 3 4 [1] [0,0,0,0,4] 4 6 [2,0,0,0,0,2] 48 2A2+2T1 G2 1 2 [1,3,3] [0,1,1] 2 7 [0,0,1,0,1,0] 50 2A1+A2+2T1 A1+T1 2 3 [1] [0,0,0,0,0,3] 3 8 [1,2,0,0,0,1] 52 A3+3T1 B2+T1 2 4 [1] [0,0,0,0,2,2] 4 9 [1,0,0,1,0,1] 54 A1+2A2+T1 A1 2 2 [1,3,3] [0,0,0,0,2] 2 10 [0,1,1,0,1,0] 56 A1+A3+2T1 A1+T1 2 4 [1] [0,0,0,0,4] 4 11 [0,0,0,2,0,0] 58 D4+2T1 2T1 1 4 [1,2,3] [0,0,3] 3 12 [2,2,0,0,0,2] 60 A4+2T1 A1+T1 2 3 [1] [0,1,2] 3 13 [0,2,0,2,0,0] 60 D4+2T1 A2 3 2 [1] [0,0,2] 2 14 [1,1,1,0,1,1] 62 A1+A4+T1 T1 1 2 [1] [0,0,0,0,2] 2 15 [1,2,1,0,1,1] 64 D5+T1 T1 1 2 [1] [0,0,0,0,0,2] 2 16 [2,1,1,0,1,2] 64 A5+T1 A1 2 2 [1,3,3] [0,0,0,0,2] 2 17 [2,0,0,2,0,2] 66 E6 e 1 1 [1,2,3,3,6,6] [0,0,2] 2 18 [2,2,0,2,0,2] 68 D5+T1 T1 1 2 [1] [0,0,2] 2 19 [2,2,2,0,2,2] 70 E6 e 1 1 [1,3,3] [0,0,1] 1 20 [2,2,2,2,2,2] 72 E6 e 1 1 [1,3,3] [0,0,1] 1 Information about orbit centralizers: orbit#: 0 diagram: [0,0,0,0,0,0] isogeny information: Centralizer: E6 Group is semisimple center=Z/3Z simply connected root datum of Lie type 'E6' ------------- orbit#: 1 diagram: [0,1,0,0,0,0] isogeny information: Centralizer: A5 Group is semisimple center=Z/6Z simply connected root datum of Lie type 'A5' ------------- orbit#: 2 diagram: [1,0,0,0,0,1] isogeny information: Centralizer: B3+T1 Center is a connected complex torus of rank 1 simply connected root datum of Lie type 'B3' ------------- orbit#: 3 diagram: [0,0,0,1,0,0] isogeny information: Centralizer: A1+A2 Group is semisimple center=Z/6Z simply connected root datum of Lie type 'A2' simply connected root datum of Lie type 'A1' ------------- orbit#: 4 diagram: [0,2,0,0,0,0] isogeny information: Centralizer: 2A2 Group is semisimple center=Z/3Z x Z/3Z simply connected root datum of Lie type 'A2' simply connected root datum of Lie type 'A2' ------------- orbit#: 5 diagram: [1,1,0,0,0,1] isogeny information: Centralizer: A2+T1 Split exact sequence: 1->S->Z->Z/S->1 S=complex torus of rank 1 Z/S=Center(G/S)=Z/3Z simply connected root datum of Lie type 'A2' ------------- orbit#: 6 diagram: [2,0,0,0,0,2] isogeny information: Centralizer: G2 Center is trivial simply connected adjoint root datum of Lie type 'G2' ------------- orbit#: 7 diagram: [0,0,1,0,1,0] isogeny information: Centralizer: A1+T1 Center is a connected complex torus of rank 1 simply connected root datum of Lie type 'A1' ------------- orbit#: 8 diagram: [1,2,0,0,0,1] isogeny information: Centralizer: B2+T1 Center is a connected complex torus of rank 1 simply connected root datum of Lie type 'B2' ------------- orbit#: 9 diagram: [1,0,0,1,0,1] isogeny information: Centralizer: A1 Group is semisimple center=Z/2Z simply connected root datum of Lie type 'A1' ------------- orbit#: 10 diagram: [0,1,1,0,1,0] isogeny information: Centralizer: A1+T1 Split exact sequence: 1->S->Z->Z/S->1 S=complex torus of rank 1 Z/S=Center(G/S)=Z/2Z simply connected root datum of Lie type 'A1' ------------- orbit#: 11 diagram: [0,0,0,2,0,0] isogeny information: Centralizer: 2T1 Center is a connected complex torus of rank 2 ------------- orbit#: 12 diagram: [2,2,0,0,0,2] isogeny information: Centralizer: A1+T1 Center is a connected complex torus of rank 1 simply connected root datum of Lie type 'A1' ------------- orbit#: 13 diagram: [0,2,0,2,0,0] isogeny information: Centralizer: A2 Group is semisimple center=Z/3Z simply connected root datum of Lie type 'A2' ------------- orbit#: 14 diagram: [1,1,1,0,1,1] isogeny information: Centralizer: T1 Center is a connected complex torus of rank 1 ------------- orbit#: 15 diagram: [1,2,1,0,1,1] isogeny information: Centralizer: T1 Center is a connected complex torus of rank 1 ------------- orbit#: 16 diagram: [2,1,1,0,1,2] isogeny information: Centralizer: A1 Group is semisimple center=Z/2Z simply connected root datum of Lie type 'A1' ------------- orbit#: 17 diagram: [2,0,0,2,0,2] isogeny information: Centralizer: e Center is trivial ------------- orbit#: 18 diagram: [2,2,0,2,0,2] isogeny information: Centralizer: T1 Center is a connected complex torus of rank 1 ------------- orbit#: 19 diagram: [2,2,2,0,2,2] isogeny information: Centralizer: e Center is trivial ------------- orbit#: 20 diagram: [2,2,2,2,2,2] isogeny information: Centralizer: e Center is trivial ------------- Arthur parameters listed by orbit: #parameters by orbit: [3,4,5,4,4,4,2,3,4,2,4,3,3,2,2,2,2,2,2,1,1] Total: 59 orbit #0 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 0, 0, 0, 0, 0, 0 ] [0,0,0,0,0,0] 0 1 root datum of Lie type 'D5.T1' [ 0, 0, 0, 0, 0, 0 ] [0,0,0,0,0] 0 1 root datum of Lie type 'A5.A1' [ 0, 0, 0, 0, 0, 0 ] [0,0,0,0,0,0] 0 1 orbit #1 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 1, 2, 2, 3, 2, 1 ] [0,1,0,0,0,0] 22 1 root datum of Lie type 'D5.T1' [ 1, 2, 2, 3, 2, 1 ] [0,1,0,0,0] 14 1 root datum of Lie type 'A5.A1' [ 0, 1, 1, 1, 1, 0 ] [0,0,0,0,0,2] 2 1 root datum of Lie type 'A5.A1' [ 1, 1, 2, 3, 2, 1 ] [0,0,1,1,0,0] 10 1 orbit #2 for G #orbits for (disconnected) Cent(O): 5 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 2, 2, 3, 4, 3, 2 ] [1,0,0,0,0,1] 32 1 root datum of Lie type 'D5.T1' [ 1, 2, 2, 4, 3, 1 ] [0,0,0,2,0] 16 1 root datum of Lie type 'D5.T1' [ 2, 2, 3, 4, 3, 2 ] [1,0,0,0,1] 20 1 root datum of Lie type 'A5.A1' [ 1, 2, 3, 4, 3, 1 ] [0,0,1,1,0,2] 12 1 root datum of Lie type 'A5.A1' [ 2, 2, 3, 4, 3, 2 ] [1,0,0,0,1,0] 16 1 orbit #3 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 2, 3, 4, 6, 4, 2 ] [0,0,0,1,0,0] 40 1 root datum of Lie type 'D5.T1' [ 2, 3, 4, 6, 4, 2 ] [0,0,1,1,0] 24 1 root datum of Lie type 'A5.A1' [ 2, 3, 3, 5, 3, 2 ] [0,2,0,0,0,0] 18 1 root datum of Lie type 'A5.A1' [ 2, 3, 4, 5, 4, 2 ] [1,0,0,0,1,2] 18 1 orbit #4 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 2, 4, 4, 6, 4, 2 ] [0,2,0,0,0,0] 42 1 root datum of Lie type 'D5.T1' [ 2, 4, 4, 6, 4, 2 ] [0,2,0,0,0] 26 1 root datum of Lie type 'A5.A1' [ 2, 2, 4, 6, 4, 2 ] [0,0,2,2,0,0] 18 1 root datum of Lie type 'A5.A1' [ 2, 4, 4, 6, 4, 2 ] [0,2,0,0,0,2] 20 1 orbit #5 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 3, 4, 5, 7, 5, 3 ] [1,1,0,0,0,1] 46 1 root datum of Lie type 'D5.T1' [ 3, 4, 5, 7, 5, 3 ] [1,1,0,0,1] 28 1 root datum of Lie type 'A5.A1' [ 2, 3, 5, 7, 5, 2 ] [0,0,2,2,0,2] 20 1 root datum of Lie type 'A5.A1' [ 3, 3, 5, 7, 5, 3 ] [1,0,1,1,1,0] 22 1 orbit #6 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 4, 4, 6, 8, 6, 4 ] [2,0,0,0,0,2] 48 1 root datum of Lie type 'A5.A1' [ 4, 4, 6, 8, 6, 4 ] [2,0,0,0,2,0] 24 1 orbit #7 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 3, 4, 6, 8, 6, 3 ] [0,0,1,0,1,0] 50 1 root datum of Lie type 'D5.T1' [ 3, 4, 6, 8, 5, 3 ] [0,0,2,0,0] 30 1 root datum of Lie type 'A5.A1' [ 3, 4, 6, 8, 6, 3 ] [1,0,1,1,1,2] 24 1 orbit #8 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 4, 6, 7, 10, 7, 4 ] [1,2,0,0,0,1] 52 1 root datum of Lie type 'D5.T1' [ 3, 6, 6, 10, 7, 3 ] [0,2,0,2,0] 28 1 root datum of Lie type 'D5.T1' [ 4, 6, 7, 10, 7, 4 ] [1,2,0,0,1] 32 1 root datum of Lie type 'A5.A1' [ 4, 4, 7, 10, 7, 4 ] [1,0,2,2,1,0] 24 1 orbit #9 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 4, 5, 7, 10, 7, 4 ] [1,0,0,1,0,1] 54 1 root datum of Lie type 'A5.A1' [ 4, 5, 7, 9, 7, 4 ] [2,0,0,0,2,2] 26 1 orbit #10 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 4, 6, 8, 11, 8, 4 ] [0,1,1,0,1,0] 56 1 root datum of Lie type 'D5.T1' [ 4, 6, 7, 11, 8, 4 ] [1,1,0,2,1] 32 1 root datum of Lie type 'A5.A1' [ 4, 5, 7, 11, 7, 4 ] [0,2,2,2,0,0] 26 1 root datum of Lie type 'A5.A1' [ 4, 5, 8, 11, 8, 4 ] [1,0,2,2,1,2] 26 1 orbit #11 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 4, 6, 8, 12, 8, 4 ] [0,0,0,2,0,0] 58 1 root datum of Lie type 'D5.T1' [ 4, 6, 8, 12, 8, 4 ] [0,0,2,2,0] 34 1 root datum of Lie type 'A5.A1' [ 4, 6, 8, 12, 8, 4 ] [0,2,2,2,0,2] 28 1 orbit #12 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 6, 8, 10, 14, 10, 6 ] [2,2,0,0,0,2] 60 1 root datum of Lie type 'D5.T1' [ 6, 8, 10, 14, 10, 6 ] [2,2,0,0,2] 36 1 root datum of Lie type 'A5.A1' [ 6, 6, 10, 14, 10, 6 ] [2,0,2,2,2,0] 28 1 orbit #13 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 6, 10, 12, 18, 12, 6 ] [0,2,0,2,0,0] 60 1 root datum of Lie type 'D5.T1' [ 6, 10, 12, 18, 12, 6 ] [0,2,2,2,0] 36 1 orbit #14 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 6, 8, 11, 15, 11, 6 ] [1,1,1,0,1,1] 62 1 root datum of Lie type 'A5.A1' [ 6, 7, 11, 15, 11, 6 ] [2,0,2,2,2,2] 30 1 orbit #15 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 7, 10, 13, 18, 13, 7 ] [1,2,1,0,1,1] 64 1 root datum of Lie type 'D5.T1' [ 7, 10, 12, 18, 13, 7 ] [2,2,0,2,2] 38 1 orbit #16 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 8, 10, 14, 19, 14, 8 ] [2,1,1,0,1,2] 64 1 root datum of Lie type 'A5.A1' [ 8, 9, 13, 19, 13, 8 ] [2,2,2,2,2,0] 30 1 orbit #17 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 8, 10, 14, 20, 14, 8 ] [2,0,0,2,0,2] 66 1 root datum of Lie type 'A5.A1' [ 8, 10, 14, 20, 14, 8 ] [2,2,2,2,2,2] 32 1 orbit #18 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 10, 14, 18, 26, 18, 10 ] [2,2,0,2,0,2] 68 1 root datum of Lie type 'D5.T1' [ 10, 14, 18, 26, 18, 10 ] [2,2,2,2,2] 40 1 orbit #19 for G #orbits for (disconnected) Cent(O): 1 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 12, 16, 22, 30, 22, 12 ] [2,2,2,0,2,2] 70 1 orbit #20 for G #orbits for (disconnected) Cent(O): 1 K_0 H diagram dim mult simply connected root datum of Lie type 'E6' [ 16, 22, 30, 42, 30, 16 ] [2,2,2,2,2,2] 72 1 orbit |packet| 13 1 18 1 20 1 Total 3 *: dual(cell) contains an Aq(lambda) orbit# block# cell# parameters 13 0 0 1 18 0 1 1 20 0 2 1 Total 3 orbit# block# cell# parameters inf. char. 13 0 0 final parameter(x=0,lambda=[3,5,6,9,6,3]/1,nu=[0,0,0,0,0,0]/1)(I) [ 3, 5, 6, 9, 6, 3 ]/1 18 0 1 final parameter(x=31,lambda=[6,9,11,17,11,6]/1,nu=[2,4,4,8,4,2]/1)(I) [ 5, 7, 9, 13, 9, 5 ]/1 20 0 2 final parameter(x=44,lambda=[8,11,15,21,15,8]/1,nu=[8,8,12,16,12,8]/1) [ 8, 11, 15, 21, 15, 8 ]/1 Total 3 Induced 2 set parameters=[ parameter(G,0,[ 3, 5, 6, 9, 6, 3 ]/1,[ 0, 0, 0, 0, 0, 0 ]/1), parameter(G,31,[ 6, 9, 11, 17, 11, 6 ]/1,[ 2, 4, 4, 8, 4, 2 ]/1), parameter(G,44,[ 8, 11, 15, 21, 15, 8 ]/1,[ 8, 8, 12, 16, 12, 8 ]/1) ]