ABSTRACT

ItisfairlyeasytoseethattheactionofOU(u,z)on'Je®S(g'_)is welldefined,andonecanintroduceitsLaurentcoefficients

theclosedintegrationcontourpositivelyencirclingz=0. Proposition10.TheLaurentcoefficientsE~satisfythefollowingcommutationrelations:

PROOF.Thepropositionfollowsfromanexplicitcomputationof thecommutator[61].AsaconsequenceoftheCampbell-Baker-Hausdorff formula,onehas

!Jbeinggivenby m

•(T(U)(T(~)zmBpw;O(haJUmBpw;<Xh~J®:"'f(u,z)"'f(~,u): Bystandardarguments,theintegrationcontourcanbecontinuouslydeformedsothat

..(I)2~~dzf.du..[£~,£113)=- -.LJ-- z'ul!J2t7Tr=l0ZE-rzU wheretheuintegrationisperformedonacontourpositivelyencirclingu =£-rz,excludingu=0.Toperformthisintegration,onehastotake