POINTED REPRESENTATIONS OF INFINITE DIMENSIONAL LIE ALGEBRAS

(整期优先)网络出版时间:1995-02-12
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AcontravariantbilinearpairingKoneveryM(ρ)×M(ρθ)isdeterminedanditisprovedthatM(ρ)isirreducibleifandonlyifKisleftnondegenerate,ItisalsoprovedthateverycyclicpointedmoduleisaquotientofsomeVerma-likepointedmodule;moreoverifitisirreduciblethenitisaquotientoftheVerma-likepointedmodulebytheleftkernelofsomebilinearpairingK.Incasethemassfunctionissymmetric,thereexistsabilinearformonM(ρ),Itisprovedthatunitarypointedmodulesareintegrable,Inaddition,acharacterizationofthemassfunctionsofKac-Moodyalgebrasisgiven,whichisageneralizationofthefinitedimensionalLiealgebrascase.