LOOP GROUPS, INTEGRABLE SYSTEMS, AND RANK 2 EXTENSIONS 39

the Hamiltonian

/

zoo

tr F{A)-

-too •••

2cfA

generates a flow

where

dAF(t,X)

Jt

[(Tr-F(AF(t,.)))(\),AF(t,\)}

AHt^^-^l-^22

, MFii)eo2{Ny

1-A

Differentiation with respect to A at A = 0 again gives

dMF(t)

dt

[{K-F'{AF{t,.))m,MF{t)} .

/

ir

' denote integration along the indented contour

-ir

I

P

(2.132)

(2.133)

(2.134)

(2.135)

Figure 2.1

As F is real analytic, we find

(7r_F(A

P

))(0)=y'F'(.4

F

(t,A))i

On the other hand a Hamiltonian H on 02(N)* generates the flow

dM

A

dt

[ T T

0

V # ( M ) , M ] .

(2.136)

(2.137)