Information about orbit centralizers:
for E6 adjoint
(this information is used on the dual side,
for G simply connected, G^\vee adjoint)

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'
-------------
Gorbit#: 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