简介：AcontravariantbilinearpairingKoneveryM(ρ）×M（ρθ)isdeterminedanditisprovedthatM(ρ)isirreducibleifandonlyifKisleftnondegenerate,ItisalsoprovedthateverycyclicpointedmoduleisaquotientofsomeVerma-likepointedmodule;moreoverifitisirreduciblethenitisaquotientoftheVerma-likepointedmodulebytheleftkernelofsomebilinearpairingK.Incasethemassfunctionissymmetric,thereexistsabilinearformonM(ρ),Itisprovedthatunitarypointedmodulesareintegrable,Inaddition,acharacterizationofthemassfunctionsofKac-Moodyalgebrasisgiven,whichisageneralizationofthefinitedimensionalLiealgebrascase.

简介：Inthispaper,weconstructanoperatorwhichhasalgebraicprecisionofpointedorderandapproximatestofC[0,1]uniformlyon[0,1].