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: (simply connected root datum of Lie type 'E6',(),[ 16, 22, 30, 42, 30, 16 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 12, 16, 22, 30, 22, 12 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 1, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 10, 14, 18, 26, 18, 10 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 0, 0, 0, 0, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 8, 10, 14, 20, 14, 8 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 1, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 8, 10, 14, 20, 14, 8 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 2, 0, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 7, 10, 13, 18, 13, 7 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 1, 0, 0, 0, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 6, 10, 12, 18, 12, 6 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 0, 0, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 6, 8, 11, 15, 11, 6 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 0, 1, 0, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 6, 8, 10, 14, 10, 6 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 2, 0, 0, 0, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 6, 8, 12, 8, 4 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 0, 0, 1, 0, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 6, 8, 12, 8, 4 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 1, 1, 0, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 6, 8, 12, 8, 4 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 0, 0, 0, 2, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 6, 7, 10, 7, 4 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 2, 2, 0, 0, 0, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 4, 6, 8, 6, 4 ]) Computing weak packet for orbit: adjoint root datum of Lie type 'E6' [ 0, 2, 0, 2, 0, 0 ] dim=60 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 2, 3, 2, 3, 2, 2 ]/1 gamma_final:[ 0, 1, 0, 1, 0, 0 ]/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:simply connected 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=[2,3,2,3,2,2]/1,nu=[0,0,0,0,0,0]/1) [ 0, 1, 0, 1, 0, 0 ]/1 cell character: 13 springer_O:13 dim: 20 24 dim: 1 24 Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 4, 5, 7, 10, 7, 4 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 1, 1, 0, 1, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 3, 4, 5, 7, 5, 3 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 1, 2, 1, 0, 1, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 2, 4, 4, 6, 4, 2 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 2, 1, 1, 0, 1, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 2, 4, 4, 6, 4, 2 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 2, 0, 0, 2, 0, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 2, 2, 3, 4, 3, 2 ]) Computing weak packet for orbit: adjoint root datum of Lie type 'E6' [ 2, 2, 0, 2, 0, 2 ] dim=68 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 3, 3, 2, 3, 2, 3 ]/1 gamma_final:[ 1, 1, 0, 1, 0, 1 ]/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:simply connected 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=[3,3,2,3,2,3]/1,nu=[0,0,0,0,0,0]/1) [ 1, 1, 0, 1, 0, 1 ]/1 survive:final parameter(x=2,lambda=[1,3,3,3,3,1]/1,nu=[6,0,-3,0,-3,6]/2) [ 1, 1, 0, 1, 0, 1 ]/1 survive:final parameter(x=13,lambda=[0,9,5,-3,5,0]/1,nu=[4,-8,-4,8,-4,4]/1) [ 1, 1, 0, 1, 0, 1 ]/1 survive:final parameter(x=19,lambda=[-1,-5,6,3,6,-1]/1,nu=[11,22,-11,0,-11,11]/2) [ 1, 1, 0, 1, 0, 1 ]/1 survive:final parameter(x=31,lambda=[3,3,7,-7,7,3]/1,nu=[0,0,-8,16,-8,0]/1) [ 1, 1, 0, 1, 0, 1 ]/1 cell character: 10 springer_O:10 dim: 1 20 Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 1, 2, 2, 3, 2, 1 ]) Skipping dual orbit (adjoint root datum of Lie type 'E6',(),[ 2, 2, 2, 0, 2, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (simply connected root datum of Lie type 'E6',(),[ 0, 0, 0, 0, 0, 0 ]) Computing weak packet for orbit: adjoint root datum of Lie type 'E6' [ 2, 2, 2, 2, 2, 2 ] dim=72 Computing weak packets for connected real group with Lie algebra 'e6(f4)' gamma:[ 3, 3, 3, 3, 3, 3 ]/1 gamma_final:[ 1, 1, 1, 1, 1, 1 ]/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:simply connected 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=[3,3,3,3,3,3]/1,nu=[0,0,0,0,0,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=1,lambda=[4,3,1,5,1,4]/1,nu=[-3,0,6,-6,6,-3]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=2,lambda=[1,3,4,3,4,1]/1,nu=[6,0,-3,0,-3,6]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=3,lambda=[5,7,3,-1,3,5]/1,nu=[-3,-6,0,6,0,-3]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=4,lambda=[3,3,0,6,3,0]/1,nu=[0,0,9,-9,0,9]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=5,lambda=[0,3,3,6,0,3]/1,nu=[9,0,0,-9,9,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=6,lambda=[4,8,3,-2,7,-1]/1,nu=[-3,-15,0,15,-12,12]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=7,lambda=[6,-3,3,3,3,6]/1,nu=[-9,18,0,0,0,-9]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=8,lambda=[-1,8,7,-2,3,4]/1,nu=[12,-15,-12,15,0,-3]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=9,lambda=[1,3,1,7,1,1]/1,nu=[3,0,3,-6,3,3]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=10,lambda=[3,9,3,3,-3,3]/1,nu=[0,-9,0,0,9,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=11,lambda=[3,9,-3,3,3,3]/1,nu=[0,-9,9,0,0,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=12,lambda=[5,-4,3,3,8,-2]/1,nu=[-6,21,0,0,-15,15]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=13,lambda=[0,9,6,-3,6,0]/1,nu=[9,-18,-9,18,-9,9]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=14,lambda=[-2,-4,8,3,3,5]/1,nu=[15,21,-15,0,0,-6]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=15,lambda=[3,10,-2,1,5,1]/1,nu=[0,-21,15,6,-6,6]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=16,lambda=[4,-5,3,10,-4,3]/1,nu=[-3,24,0,-21,21,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=17,lambda=[3,-5,-4,10,3,4]/1,nu=[0,24,21,-21,0,-3]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=18,lambda=[1,10,5,1,-2,3]/1,nu=[6,-21,-6,6,15,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=19,lambda=[-1,-5,7,3,7,-1]/1,nu=[6,12,-6,0,-6,6]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=20,lambda=[3,3,12,-6,3,3]/1,nu=[0,0,-27,27,0,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=21,lambda=[3,3,3,-6,12,3]/1,nu=[0,0,0,27,-27,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=23,lambda=[3,-6,-3,9,6,0]/1,nu=[0,27,18,-18,-9,9]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=24,lambda=[0,-6,6,9,-3,3]/1,nu=[9,27,-9,-18,18,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=22,lambda=[3,11,-1,3,-1,3]/1,nu=[0,-12,6,0,6,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=25,lambda=[3,4,3,3,-8,13]/1,nu=[0,-3,0,0,33,-30]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=26,lambda=[13,4,-8,3,3,3]/1,nu=[-30,-3,33,0,0,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=27,lambda=[3,1,3,-5,13,1]/1,nu=[0,3,0,12,-15,3]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=28,lambda=[3,-7,-2,13,-2,3]/1,nu=[0,30,15,-30,15,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=29,lambda=[1,1,13,-5,3,3]/1,nu=[3,3,-15,12,0,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=30,lambda=[3,3,3,3,3,-9]/1,nu=[0,0,0,0,0,18]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=31,lambda=[3,3,9,-9,9,3]/1,nu=[0,0,-9,18,-9,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=32,lambda=[3,0,3,6,-9,12]/1,nu=[0,9,0,-9,36,-27]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=33,lambda=[12,0,-9,6,3,3]/1,nu=[-27,9,36,-9,0,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=34,lambda=[-9,3,3,3,3,3]/1,nu=[18,0,0,0,0,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=35,lambda=[3,3,8,-2,-5,11]/1,nu=[0,0,-15,15,24,-24]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=36,lambda=[11,3,-5,-2,8,3]/1,nu=[-24,0,24,15,-15,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=37,lambda=[3,1,3,5,1,-8]/1,nu=[0,6,0,-6,6,33]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=38,lambda=[-8,1,1,5,3,3]/1,nu=[33,6,6,-6,0,0]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=39,lambda=[3,3,7,-1,3,-7]/1,nu=[0,0,-6,6,0,15]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=40,lambda=[10,3,-4,3,-4,10]/1,nu=[-21,0,21,0,21,-21]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=41,lambda=[-7,3,3,-1,7,3]/1,nu=[15,0,0,6,-6,0]/1) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=42,lambda=[9,3,-3,3,3,-6]/1,nu=[-18,0,18,0,0,27]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=43,lambda=[-6,3,3,3,-3,9]/1,nu=[27,0,0,0,18,-18]/2) [ 1, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=44,lambda=[-5,3,3,3,3,-5]/1,nu=[12,0,0,0,0,12]/1) [ 1, 1, 1, 1, 1, 1 ]/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',(),[ 0, 10, 10, 18, 14, 8 ]) 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',(),[ 0, 7, 7, 12, 10, 6 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -1, 0, 0, 0, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 6, 6, 12, 10, 6 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -1, 0, 0, 0, 0, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 6, 6, 10, 8, 4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -2, 1, 1, 0, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 8, 6, 4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -2, 0, 0, 1, 0, 1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 8, 6, 4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -2, 0, 0, 0, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 6, 6, 4 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -3, 0, 0, 0, 2, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 4, 4, 7, 6, 3 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -3, 1, 1, 0, 1, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 6, 4, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -3, 0, 0, 2, 0, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 3, 3, 5, 4, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -4, 1, 1, 0, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 4, 4, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -4, 1, 1, 0, 1, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 4, 4, 2 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -4, 0, 0, 2, 0, 2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 2, 2, 2 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ -6, 0, 0, 2, 2, 2 ] dim=36 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ -13, 2, 2, 3, 3, 3 ]/1 gamma_final:[ -3, 0, 0, 1, 1, 1 ]/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=[-13,2,2,3,3,3]/1,nu=[0,0,0,0,0,0]/1) [ -3, 0, 0, 1, 1, 1 ]/1 cell character: 12 springer_O:12 dim: 1 4 Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 3, 2, 1 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -6, 2, 2, 0, 2, 0 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 2, 2, 1 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ -7, 2, 2, 0, 2, 2 ]) (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' [ -10, 2, 2, 2, 2, 2 ] dim=40 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ -15, 3, 3, 3, 3, 3 ]/1 gamma_final:[ -5, 1, 1, 1, 1, 1 ]/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=[-15,3,3,3,3,3]/1,nu=[0,0,0,0,0,0]/1) [ -5, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=1,lambda=[-14,1,1,5,3,3]/1,nu=[-3,6,6,-6,0,0]/2) [ -5, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=2,lambda=[-13,3,3,-1,7,3]/1,nu=[-3,0,0,6,-6,0]/1) [ -5, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=3,lambda=[-12,3,3,3,-3,9]/1,nu=[-9,0,0,0,18,-18]/2) [ -5, 1, 1, 1, 1, 1 ]/1 survive:final parameter(x=4,lambda=[-11,3,3,3,3,-5]/1,nu=[-6,0,0,0,0,12]/1) [ -5, 1, 1, 1, 1, 1 ]/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',(),[ 8, 10, 14, 18, 10, 0 ]) 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',(),[ 6, 7, 10, 12, 7, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 0, 1, 0, 0, -1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 6, 6, 10, 12, 6, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 0, 0, 0, 0, -1 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 4, 6, 8, 10, 6, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 1, 0, 0, 1, -2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 4, 4, 6, 8, 4, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 1, 0, 0, 1, 0, -2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 4, 4, 6, 8, 4, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 0, 2, 0, 0, -2 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 3, 4, 6, 7, 4, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 1, 1, 0, 1, -3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 4, 3, 6, 6, 3, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 0, 2, 0, 0, -3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 3, 4, 6, 3, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 0, 0, 2, 0, -3 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 3, 4, 5, 3, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 1, 2, 0, 1, -4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 2, 4, 4, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 1, 1, 0, 1, -4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 2, 4, 4, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 0, 0, 2, 0, -4 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 1, 2, 2, 3, 2, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 0, 2, 2, 0, 2, -6 ]) (d(O_check) has no real forms for G) Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 2, 1, 2, 2, 1, 0 ]) Computing weak packet for orbit: root datum of Lie type 'D5.T1' [ 2, 0, 2, 2, 0, -6 ] dim=36 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 3, 2, 3, 3, 2, -13 ]/1 gamma_final:[ 1, 0, 1, 1, 0, -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=[3,2,3,3,2,-13]/1,nu=[0,0,0,0,0,0]/1) [ 1, 0, 1, 1, 0, -3 ]/1 cell character: 12 springer_O:12 dim: 1 4 Orbit by diagram: (root datum of Lie type 'D5.T1',(),[ 1, 1, 2, 2, 1, 0 ]) Skipping dual orbit (root datum of Lie type 'D5.T1',(),[ 2, 2, 2, 0, 2, -7 ]) (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' [ 2, 2, 2, 2, 2, -10 ] dim=40 Computing weak packets for connected real group with Lie algebra 'so(9,1).gl(1,R)' gamma:[ 3, 3, 3, 3, 3, -15 ]/1 gamma_final:[ 1, 1, 1, 1, 1, -5 ]/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=[3,3,3,3,3,-15]/1,nu=[0,0,0,0,0,0]/1) [ 1, 1, 1, 1, 1, -5 ]/1 survive:final parameter(x=1,lambda=[3,1,3,5,1,-14]/1,nu=[0,6,0,-6,6,-3]/2) [ 1, 1, 1, 1, 1, -5 ]/1 survive:final parameter(x=2,lambda=[3,3,7,-1,3,-13]/1,nu=[0,0,-6,6,0,-3]/1) [ 1, 1, 1, 1, 1, -5 ]/1 survive:final parameter(x=3,lambda=[9,3,-3,3,3,-12]/1,nu=[-18,0,18,0,0,-9]/2) [ 1, 1, 1, 1, 1, -5 ]/1 survive:final parameter(x=4,lambda=[-5,3,3,3,3,-11]/1,nu=[12,0,0,0,0,-6]/1) [ 1, 1, 1, 1, 1, -5 ]/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: adjoint 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 1 3 [1] [1,1,1] 3 1 [0,1,0,0,0,0] 22 A1+5T1 A5 2 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 2 4 [1] [0,0,0,0,4] 4 4 [0,2,0,0,0,0] 42 A2+4T1 2A2 3 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] [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] [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 1 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] [0,0,0,0,2] 2 17 [2,0,0,2,0,2] 66 E6 e 1 1 [1,2] [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] [0,0,1] 1 20 [2,2,2,2,2,2] 72 E6 e 1 1 [1] [0,0,1] 1 Information about orbit centralizers: orbit#: 0 diagram: [0,0,0,0,0,0] isogeny information: Centralizer: E6 Center is trivial adjoint root datum of Lie type 'E6' ------------- orbit#: 1 diagram: [0,1,0,0,0,0] isogeny information: Centralizer: A5 Group is semisimple center=Z/2Z 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/2Z adjoint 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 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 Center is a connected complex torus of rank 1 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 Center is trivial adjoint 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 adjoint 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 adjoint root datum of Lie type 'E6' [ 0, 1, 0, 0, 0, 0 ] [0,1,0,0,0,0] 22 1 root datum of Lie type 'D5.T1' [ 0, 1, 0, 0, 0, 0 ] [0,1,0,0,0] 14 1 root datum of Lie type 'A5.A1' [ -1, 1, 1, -1, 1, -1 ] [0,0,0,0,0,2] 2 1 root datum of Lie type 'A5.A1' [ 0, -1, 0, 1, 0, 0 ] [0,0,1,1,0,0] 10 1 orbit #2 for G #orbits for (disconnected) Cent(O): 5 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 0, 0, 0, 0, 1 ] [1,0,0,0,0,1] 32 1 root datum of Lie type 'D5.T1' [ 0, 0, -1, 1, 1, -1 ] [0,0,0,2,0] 16 1 root datum of Lie type 'D5.T1' [ 1, 0, 0, 0, 0, 1 ] [1,0,0,0,1] 20 1 root datum of Lie type 'A5.A1' [ -1, 0, 1, 0, 1, -1 ] [0,0,1,1,0,2] 12 1 root datum of Lie type 'A5.A1' [ 1, 0, 0, 0, 0, 1 ] [1,0,0,0,1,0] 16 1 orbit #3 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 0, 0, 1, 0, 0 ] [0,0,0,1,0,0] 40 1 root datum of Lie type 'D5.T1' [ 0, 0, 0, 1, 0, 0 ] [0,0,1,1,0] 24 1 root datum of Lie type 'A5.A1' [ 1, 1, -1, 1, -1, 1 ] [0,2,0,0,0,0] 18 1 root datum of Lie type 'A5.A1' [ 0, 1, 1, -1, 1, 0 ] [1,0,0,0,1,2] 18 1 orbit #4 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 2, 0, 0, 0, 0 ] [0,2,0,0,0,0] 42 1 root datum of Lie type 'D5.T1' [ 0, 2, 0, 0, 0, 0 ] [0,2,0,0,0] 26 1 root datum of Lie type 'A5.A1' [ 0, -2, 0, 2, 0, 0 ] [0,0,2,2,0,0] 18 1 root datum of Lie type 'A5.A1' [ 0, 2, 0, 0, 0, 0 ] [0,2,0,0,0,2] 20 1 orbit #5 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 1, 0, 0, 0, 1 ] [1,1,0,0,0,1] 46 1 root datum of Lie type 'D5.T1' [ 1, 1, 0, 0, 0, 1 ] [1,1,0,0,1] 28 1 root datum of Lie type 'A5.A1' [ -1, -1, 1, 1, 1, -1 ] [0,0,2,2,0,2] 20 1 root datum of Lie type 'A5.A1' [ 1, -1, 0, 1, 0, 1 ] [1,0,1,1,1,0] 22 1 orbit #6 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 0, 0, 0, 0, 2 ] [2,0,0,0,0,2] 48 1 root datum of Lie type 'A5.A1' [ 2, 0, 0, 0, 0, 2 ] [2,0,0,0,2,0] 24 1 orbit #7 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 0, 1, 0, 1, 0 ] [0,0,1,0,1,0] 50 1 root datum of Lie type 'D5.T1' [ 0, 0, 1, 1, -1, 1 ] [0,0,2,0,0] 30 1 root datum of Lie type 'A5.A1' [ 0, 0, 1, 0, 1, 0 ] [1,0,1,1,1,2] 24 1 orbit #8 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 2, 0, 0, 0, 1 ] [1,2,0,0,0,1] 52 1 root datum of Lie type 'D5.T1' [ 0, 2, -1, 1, 1, -1 ] [0,2,0,2,0] 28 1 root datum of Lie type 'D5.T1' [ 1, 2, 0, 0, 0, 1 ] [1,2,0,0,1] 32 1 root datum of Lie type 'A5.A1' [ 1, -2, 0, 2, 0, 1 ] [1,0,2,2,1,0] 24 1 orbit #9 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 0, 0, 1, 0, 1 ] [1,0,0,1,0,1] 54 1 root datum of Lie type 'A5.A1' [ 1, 1, 1, -1, 1, 1 ] [2,0,0,0,2,2] 26 1 orbit #10 for G #orbits for (disconnected) Cent(O): 4 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 1, 1, 0, 1, 0 ] [0,1,1,0,1,0] 56 1 root datum of Lie type 'D5.T1' [ 1, 1, -1, 1, 1, 0 ] [1,1,0,2,1] 32 1 root datum of Lie type 'A5.A1' [ 1, -1, -1, 3, -1, 1 ] [0,2,2,2,0,0] 26 1 root datum of Lie type 'A5.A1' [ 0, -1, 1, 1, 1, 0 ] [1,0,2,2,1,2] 26 1 orbit #11 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 0, 0, 2, 0, 0 ] [0,0,0,2,0,0] 58 1 root datum of Lie type 'D5.T1' [ 0, 0, 0, 2, 0, 0 ] [0,0,2,2,0] 34 1 root datum of Lie type 'A5.A1' [ 0, 0, 0, 2, 0, 0 ] [0,2,2,2,0,2] 28 1 orbit #12 for G #orbits for (disconnected) Cent(O): 3 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 2, 0, 0, 0, 2 ] [2,2,0,0,0,2] 60 1 root datum of Lie type 'D5.T1' [ 2, 2, 0, 0, 0, 2 ] [2,2,0,0,2] 36 1 root datum of Lie type 'A5.A1' [ 2, -2, 0, 2, 0, 2 ] [2,0,2,2,2,0] 28 1 orbit #13 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 0, 2, 0, 2, 0, 0 ] [0,2,0,2,0,0] 60 1 root datum of Lie type 'D5.T1' [ 0, 2, 0, 2, 0, 0 ] [0,2,2,2,0] 36 1 orbit #14 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 1, 1, 0, 1, 1 ] [1,1,1,0,1,1] 62 1 root datum of Lie type 'A5.A1' [ 1, -1, 1, 1, 1, 1 ] [2,0,2,2,2,2] 30 1 orbit #15 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 1, 2, 1, 0, 1, 1 ] [1,2,1,0,1,1] 64 1 root datum of Lie type 'D5.T1' [ 2, 2, -1, 1, 1, 1 ] [2,2,0,2,2] 38 1 orbit #16 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 1, 1, 0, 1, 2 ] [2,1,1,0,1,2] 64 1 root datum of Lie type 'A5.A1' [ 3, -1, -1, 3, -1, 3 ] [2,2,2,2,2,0] 30 1 orbit #17 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 0, 0, 2, 0, 2 ] [2,0,0,2,0,2] 66 1 root datum of Lie type 'A5.A1' [ 2, 0, 0, 2, 0, 2 ] [2,2,2,2,2,2] 32 1 orbit #18 for G #orbits for (disconnected) Cent(O): 2 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 2, 0, 2, 0, 2 ] [2,2,0,2,0,2] 68 1 root datum of Lie type 'D5.T1' [ 2, 2, 0, 2, 0, 2 ] [2,2,2,2,2] 40 1 orbit #19 for G #orbits for (disconnected) Cent(O): 1 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 2, 2, 0, 2, 2 ] [2,2,2,0,2,2] 70 1 orbit #20 for G #orbits for (disconnected) Cent(O): 1 K_0 H diagram dim mult adjoint root datum of Lie type 'E6' [ 2, 2, 2, 2, 2, 2 ] [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=[0,1,0,1,0,0]/1,nu=[0,0,0,0,0,0]/1)(I) [ 0, 1, 0, 1, 0, 0 ]/1 18 0 1 final parameter(x=31,lambda=[1,1,-1,3,-1,1]/1,nu=[0,0,-2,4,-2,0]/1)(I) [ 1, 1, 0, 1, 0, 1 ]/1 20 0 2 final parameter(x=44,lambda=[1,1,1,1,1,1]/1,nu=[4,0,0,0,0,4]/1) [ 1, 1, 1, 1, 1, 1 ]/1 Total 3 Induced 2 set parameters=[ parameter(G,0,[ 0, 1, 0, 1, 0, 0 ]/1,[ 0, 0, 0, 0, 0, 0 ]/1), parameter(G,31,[ 1, 1, -1, 3, -1, 1 ]/1,[ 0, 0, -2, 4, -2, 0 ]/1), parameter(G,44,[ 1, 1, 1, 1, 1, 1 ]/1,[ 4, 0, 0, 0, 0, 4 ]/1) ]