The generic automorphism phi of g_{6,16} as computed by calculautom6_16.red : phi:= [b(1,1) 0 0 0 0 0 ] [ ] [b(2,1) b(2,2) 0 0 0 0 ] [ ] [b(3,1) b(3,2) b(2,2)*b(1,1) 0 0 0 ] [ ] [ 2 ] [b(4,1) b(4,2) b(3,2)*b(1,1) b(2,2)*b(1,1) 0 0 ] [ ] [ 2 3 ] [b(5,1) b(5,2) b(4,2)*b(1,1) b(3,2)*b(1,1) b(2,2)*b(1,1) 0 ] [ ] [ 2 3 4] [b(6,1) b(6,2) b(5,2)*b(1,1) b(4,2)*b(1,1) b(3,2)*b(1,1) b(2,2)*b(1,1) ] 5 11 det(phi):=b(2,2) *b(1,1) generic derivation : delta:= mat((xi(1,1),0,0,0,0,0), (xi(2,1),xi(2,2),0,0,0,0), (xi(3,1),xi(3,2),xi(1,1) + xi(2,2),0,0,0), (xi(4,1),xi(4,2),xi(3,2),2*xi(1,1) + xi(2,2),0,0), (xi(5,1),xi(5,2),xi(4,2),xi(3,2),3*xi(1,1) + xi(2,2),0), (xi(6,1),xi(6,2),xi(5,2),xi(4,2),xi(3,2),4*xi(1,1) + xi(2,2))) [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 1 0 0 0 0] adx1 := [ ] [0 0 1 0 0 0] [ ] [0 0 0 1 0 0] [ ] [0 0 0 0 1 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] adx2 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx3 := [ ] [-1 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx4 := [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] [ ] [0 0 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx5 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [-1 0 0 0 0 0] The generic nilpotent derivation : the eigenvalues are 0 xi(1,1):=0 xi(2,2):=0 by subtracting adjoints one then may suppose: xi(3,1):=0,xi(3,2):=0,xi(4,1):=0,xi(5,1):=0,xi(6,1):=0. phi:= [b(1,1) 0 0 0 0 0 ] [ ] [b(2,1) b(2,2) 0 0 0 0 ] [ ] [b(3,1) b(3,2) b(2,2)*b(1,1) 0 0 0 ] [ ] [ 2 ] [b(4,1) b(4,2) b(3,2)*b(1,1) b(2,2)*b(1,1) 0 0 ] [ ] [ 2 3 ] [b(5,1) b(5,2) b(4,2)*b(1,1) b(3,2)*b(1,1) b(2,2)*b(1,1) 0 ] [ ] [ 2 3 4] [b(6,1) b(6,2) b(5,2)*b(1,1) b(4,2)*b(1,1) b(3,2)*b(1,1) b(2,2)*b(1,1) ] 5 11 det(phi):=b(2,2) *b(1,1) delta:= [ 0 0 0 0 0 0] [ ] [xi(2,1) 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ 0 xi(4,2) 0 0 0 0] [ ] [ 0 xi(5,2) xi(4,2) 0 0 0] [ ] [ 0 xi(6,2) xi(5,2) xi(4,2) 0 0] We denote this delta by the shortform shortformdelta:={xi(2,1), ss, xi(4,2), ss, xi(5,2), ss, xi(6,2)} paramindexeslist:={{2,1},{4,2},{5,2},{6,2}} shortformdeltaprimemodadg:={(b(2,2)*xi(2,1))/b(1,1), ss, b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=(b(2,2)*xi(2,1))/b(1,1)$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(2,2)**5*b(1,1)**11$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ b(2,2)*xi(2,1) ] [---------------- 0 0 0 0 0] [ b(1,1) ] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ 0 b(1,1) *xi(4,2) 0 0 0 0] [ ] [ 3 2 ] [ 0 b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0 0] [ ] [ 4 3 2 ] [ 0 b(1,1) *xi(6,2) b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0] ************ SUBCASE 2 : we suppose xi(2,1) = 0 *********************$ xi(2,1):=0$ shortformdeltaprimemodadg:={0, ss, b(1,1)**2*xi(4,2), ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=b(1,1)**2*xi(4,2)$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(2,2)**5*b(1,1)**11$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 2 ] [0 b(1,1) *xi(4,2) 0 0 0 0] [ ] [ 3 2 ] [0 b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0 0] [ ] [ 4 3 2 ] [0 b(1,1) *xi(6,2) b(1,1) *xi(5,2) b(1,1) *xi(4,2) 0 0] ******** SUBSUBCASE 2.2 : we suppose xi(4,2) = 0 *********************$ xi(4,2):=0$ shortformdeltaprimemodadg:={0, ss, 0, ss, b(1,1)**3*xi(5,2), ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(2,2)**5*b(1,1)**11$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 3 ] [0 b(1,1) *xi(5,2) 0 0 0 0] [ ] [ 4 3 ] [0 b(1,1) *xi(6,2) b(1,1) *xi(5,2) 0 0 0] ******** SUBSUBCASE 2.2.1. : we suppose xi(5,2) NEQ 0 *********************$ Then we can suppose xi(5,2):=1.$ xi(5,2):=1$ And we keep deltaprime(5,2):=k by taking :$ b(1,1):=k**(1/3)$ shortformdeltaprimemodadg:={0, ss, 0, ss, k, ss, k**(1/3)*xi(6,2)*k}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=k$ deltaprimemodg(6,2):=k**(1/3)*xi(6,2)*k$ det(AUTOM):=k**(2/3)*b(2,2)**5*k**3$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 k 0 0 0 0] [ ] [ 1/3 ] [0 k *xi(6,2)*k k 0 0 0] Hence, we are reduced in case 2.2.1 to:$ shortformdeltaprime ={0,SS,0,SS,1,SS,epsilon}.$ where epsilon:=xi(6,2) :=0,1.$ ******** SUBSUBCASE 2.2.2. : we suppose xi(5,2) = 0 *********************$ xi(5,2):=0$ clear b(1,1)$ shortformdeltaprimemodadg:={0, ss, 0, ss, 0, ss, b(1,1)**4*xi(6,2)}$ deltaprimemodg(2,1):=0$ deltaprimemodg(4,2):=0$ deltaprimemodg(5,2):=0$ deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$ det(AUTOM):=b(2,2)**5*b(1,1)**11$ DELTAPRIMEMODADG:= [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [ 4 ] [0 b(1,1) *xi(6,2) 0 0 0 0] Then necessarily xi(6,2) NEQ 0, hence we are reduced to :$ Hence, we are reduced in case 2.2.2 to:$ shortformdeltaprime ={0,SS,0,SS,0,SS,1}.$